GIFT  OF 


Yellow 


Yellow  and  Red 


Yellow,  Red  and  Blue 


Finished  Result 
Yellow,  Red,  Blue  and  Black 


FOUR  COLOR   PRINTING 


PRACTICAL  PHYSICS 


BY 

HENRY    S.    CARHART,    Sc.D.,    LL.D. 

\\ 

FORMERLY    PROFESSOR   OF   PHYSICS,    UNIVERSITY   OF    MICHIGAN 
AND 

HORATIO    N.   CHUTE,    M.S. 

INSTRUCTOR    IN    PHYSICS   IN   THE   ANN    ARBOR   HIGH    SCHOOL 


ALLYN    AND    BA.CON 

BOSTON  NEW  YORK  CHICAGO 

ATLANTA  SAN  FRANCISCO 


COPYRIGHT,    1920,   BY 

HENRY  S.  CARHART  AND 

HORATIO   N.   CHUTE 


XortoonD 

J.  S.  Gushing  Co.  —Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

Practical  Physics  aims  above  all  things  to  justify  its  title. 
In  introducing  an  exceptionally  large  number  of  applications, 
the  authors  have  not  lost  sight  of  the  fact  that  the  most  prac- 
tical book  is  the  one  from  which  the  pupil  can  most  easily 
learn. 

To  secure  this  practical  quality,  the  material  is  presented  in 
the  simplest  and  clearest  language :  —  short  sentences  and 
paragraphs,  terse  statements,  careful  explanations,  and  an  in- 
ductive development  of  each  principle.  The  subject  matter 
is  logically  arranged  in  the  order  followed  by  most  secondary 
schools.  Each  principle  is  illustrated  not  only  by  diagrams, 
problems,  and  questions,  but  by  its  most  striking  applications. 

While  the  number  of  these  practical  applications  is  un- 
usually large,  nothing  has  been  included  merely  because  it  is 
sensational ;  every  application  illustrates  some  principle 
treated  in  the  book.  The  utmost  care  has  been  taken  to  keep 
the  whole  work  within  easy  range  of  the  average  pupil's  ability, 
and  to  provide  material  that  can  be  easily  mastered  in  a  school 
year. 

The  World  War  has  emphasized  once  more  the  universality 
of  physics.  This  universality  is  brought  out  in  Practical 
Physics  from  the  very  outset,  always,  however,  with  care  that 
the  pupil  understand  the  basic  physical  principles  which  under- 
lie each  application. 

July  4,  1920. 


m 
459995 


CONTENTS 

Chapter  I.    Introduction  PAGE 

I.     Matter  and  Energy      .        , 1 

II.     Properties  of  Matter     .        .    ' $ 

III.     Physical  Measurements        ......       16 

Chapter  II.    Molecular  Physics 

I.     Molecular  Motion 25 

II.     Surface  Phenomena      .        .     '  .        .     .    .     ....      29 

III.     Molecular  Forces  in  Solids  .       ..     •   .        ...      34 

Chapter  III.    Mechanics  of  Fluids 

I.  Pressure  of  Fluids ,39 

II.  Bodies  Immersed  in  Liquids        .         .        .        ,  .       53 

III.  Density  and  Specific  Gravity       .               .  ._  .,  .58 

IV.  Pressure  of  the  Atmosphere         .        .-        .     '.  VV  65 
V.  Compression  and  Expansion  of  Gases          .     ,    .  ,       73 

VI.  Pneumatic  Appliances         .        .        .        .        .  .      83 

Chapter  IV.    Motion 

I.     Motion  in  Straight  Lines 91 

II.     Curvilinear  Motion      .        .         .        «        •        .        .      99 
III.     Simple  Harmonic  Motion    .        .  -     .        .        .        .     101 

Chapter  V.    Mechanics  of  Solids 

I.  Measurement  of  Force         *        .        .        •    .    •        •    104 

II.  Composition  of  Forces  and  of  Velocities     .        .        .107 

III.  Newton's  Laws  of  Motion    .        .        .        •    ;    •        •     H6 

IV.  Gravitation.        .        .        ,        ^ .122 

V.  Falling  Bodies 128 

VI.     Centripetal  and  Centrifugal  Force      .        .        .        .133 

VII.     The  Pendulum .136 

v 


VI  CONTENTS 

Chapter  VI.    Mechanical  Work  PAG, 

I.     Work  and  Energy       .        .  r        .        .        .        .     143 

II.     Machines     .        .  155 


Chapter  VII.    Sound 

I.  Wave  Motion 176 

II.  Sound  and  its  Transmission 181 

III.  Velocity  of  Sound 184 

IV.  Reflection  of  Sound 186 

V.  Resonance  .        .        .        .         .         .        .         .         .188 

VI.  Characteristics  of  Musical  Sounds      ....     191 

VII.  Interference  and  Beats 194 

VIII.  Musical  Scales    .        .        .        .        .        .        .        .196 

IX.  Vibration  of  Strings  . 201 

X.  Vibration  of  Air  in  Pipes 205 

XI.  Graphic  and  Optical  Methods 208 

Chapter  VIII.    Light 

I.  Nature  and  Transmission  of  Light    .        .        .        .    214 

II.  Photometry         .        .-      .        .        .        .        .        .219 

III.  Reflection  of  Light     .        .        .        .        .        .        .223 

IV.  Refraction  of  Light    .         .         .        .        .        .        .     238 

V.  Lenses 246 

VI.  Optical  Instruments   .......     255 

VII.  Dispersion 263 

VIII.  Color 271 

IX.  Interference  and  Diffraction  .  .     276 


Chapter  IX.    Heat 

I.  Heat  and  Temperature       ......  280 

II.     The  Thermometer 282 

III.  Expansion .287 

IV.  Measurement  of  Heat 297 

V.     Change  of  State 299 

VI.     Transmission  of  Heat 309 

VII.    Heat  and  Work.                        319 


CONTENTS  Vii 

Chapter  X.    Magnetism  PA<HS 

I.  Magnets  and  Magnetic  Action    .        .        .        .        '.  327 

II.    Nature  of  Magnetism 332 

III.  The  Magnetic  Field 333 

IV.  Terrestrial  Magnetism         .        .        .        .        .        .  336 

Chapter  XI.    Electrostatics 

I.  Electrification      .        .  • 340 

II.  Electrostatic  Induction        ...        .        .      .  .        .    344 

III.  Electrical  Distribution         .        .        ...        .346 

IV.  Electric  Potential  and  Capacity  .        ....    348 
V.  Electrical  Machines      .        .        .       >        . ..     .        .    354 

VI.  Atmospheric  Electricity       .        .        .        ...    358 

Chapter  XII.    Electric  Currents 

I.  Voltaic  Cells         .        . 361 

II.  Electrolysis  ......        .        .        .373 

III.  Ohm's  Law  and  its  Applications         .        .        .        .    378 

IV.  Heating  Effects  of  a  Current       .        .        ,        .        .385 
V.  Magnetic  Properties  of  a  Current        .     -   .        .        .    387 

VI.    Electromagnets    .        .        *        ...        .        .392 
VII.     Measuring  Instruments        ...        .        .        .    394 

Chapter  XIII.    Electromagnetic  Induction 

I.  Faraday's  Discoveries 401 

II.  Self-Induction 405 

III.  The  Induction  Coil 406 

IV.  Radioactivity  and  Electrons        .        .        '.        .        .416 

Chapter  XIV.    Dynamo-Electric  Machinery 

I.  Direct  Current  Machines 421 

II.  Alternators  and  Transformers 431 

III.  Electric  Lighting 442 

IV.  The  Electric  Telegraph 447 

V.  The  Telephone     .        .        .        .       '.        .        .        .451 

VI.     Wireless  Telegraphy 453 


yiii  CONTENTS 


Chapter  XV.    The  Motor  Car 

PAGE 

I. 
H. 

in. 

IV. 

The  Engine         .         .         .        e        .        . 
The  Storage  Battery  . 
The  Chassis  and  Running  Gear          . 
The  Brake  

460 
466 
467 

468 

V. 

The  Clutch         

469 

VI. 

Transmission  and  Differential   

470 

VII. 
VIII. 

The  Steering  Device  
The  Starter         -.         

471 
471 

IX. 

On  the  Road       .-        

472 

X. 

The  Pedestrian  

473 

Appendix 
I. 
II. 

475 
479 

Conversion  Tables      .         .         .         .         . 

in. 

Mensuration  Rules     ....... 

481 

IV. 

Table  of  Densities      

482 

V. 
Index 

Geometrical  Construction  for  Refraction  of  Light   . 

483 

1 

FULL   PAGE   ILLUSTRATIONS 

Four  Color  Process  Printing Frontispiece 


FACING   PAGE 


Electric  Welding 16 

Bureau  of  Standards,  Washington        .... 

Common  Crystals  ...  35 

Galileo  Galilei 42 

Blaise  Pascal 

Elephant  Butte  Dam     .         .         .        .         .     .    .        .'-_-••         .50 

Dry  Dock  "  Dewey  " 58 

fifi 
Hydro-airplanes • 

Motion  and  Force • 

Sir  Isaac  Newton 124 

Yosemite  Fall • 

Centrifugal  Force 

Pisa  Cathedral 

United  States  16-inch  Gun 150 

Lord  Kelvin 154 

LordRayleigh 

Photographs  of  Sound  Waves I83 

Echo  Bridge '      - 

Hermann  von  Helmholtz       . 193 

Niagara  Falls  Power  Plant   .         .         .         .         • 
Parabolic  Mirror  at  Mount  Wilson 

Moving  Picture  Film ...     258 

Various  Spectra 

Bridge  over  the  Firth  of  Forth     .... 

James  Watt 

James  Prescott  Joule     .... 

A  Row  of  Corliss  Engines     .... 

qOO 

Four-valve  Engine 

Section  and  Rotor  of  Steam  Turbine 323 

Front  and  Rear  Views  of  Airplane 

Benjamin  Franklin 358 

tx 


X  FULL  PAGE  ILLUSTRATIONS 

FACING  PAGE 

Hans  Christian  Oersted         .        .        .        «  •      .        .        .        .  366 

Alessandro  Volta „        .        .        .        .  382 

Georg  Simon  Ohm         .         .        .         .         .        .        .         .         .  382 

James  Clerk-Maxwell    .........  392 

Joseph  Henry  .      • 400 

Michael  Faraday 401 

Sir  William  Crookes      .      - 412 

Wilhelm  Konrad  Roentgen  ........  412 

Madame  Curie       .         .        .         .  .  .         .         .  418 

Sir  Joseph  John  Thomson 419 

Field  Magnet  and  Drum  Armature  of  D.  C.  Generator       .         .  426 

Electric  Engine  Crossing  the  Rockies 430 

Armature  Core  and  Field  Magnet  of  A.  C.  Generator         .         .  431 

Dam  and  Power  House,  Great  Falls,  Montana     ....  438 

Transformers  and  Switches 439 

Stator  and  Field  of  A.  C.  Generator 440 

Stator  of  Three-phase  Motor  and  Motor  Complete       .         .         .  441 

Alexander  Graham  Bell 449 

Samuel  F.  B.  Morse 449 

Field  Wireless  of  the  United  States  Army 452 

Wireless  Room  in  a  Transatlantic  Liner      .....  453 

Heinrich  Rudolf  Hertz 458 

Thomas  Alva  Edison 459 

Guglielmo  Marconi 459 


PRACTICAL  PHYSICS 


CHAPTER   I 

INTRODUCTION 

I.    MATTER  AND   ENERGY 

1.  Physics  Defined.  —  Physics  is  the  science  which  treats 
of  the  related  phenomena  of  matter  and  energy.  It  includes 
mechanics,  sound,  light,  heat,  magnetism,  and  electricity. 


A  MOTOR  CAR. 

Probably  the  automobile  is  the  best  general  application  of  the  principles 
of  physics.  Mechanics  of  solids  is  illustrated  by  its  springs,  bolts,  and  most 
of  its  moving  parts ;  mechanics  of  liquids  by  the  circulation  of  its  water- 
cooling  system  ;  sound  by  its  horn ;  light  by  its  headlights ;  heat  by  the 
explosions  of  its  engine ;  and  magnetism  and  electricity  by  its  electrical 
battery  and  its  starting  and  lighting  systems. 


:  INTRODUCTION 

r  and  fwwrgy  scarcely  admit  of  definition  except 
by  means  of  their  properties.  Matter  is  everything  we 
can  see,  taste,  or  touch,  such  as  earth,  water,  wood,  iron, 
gas  —  in  short,  everything  that  occupies  space. 

Energy  is  whatever  produces  a  change  in  the  motion  or 
condition  of  matter,  especially  against  resistance  opposing 


BRITISH  "TANK"  CROSSING  A  SHELL-HOLE. 

The  tank  is  a  land  battleship,  carrying  guns  and  running  on  its  own  track 
which  it  carries  with  it.  In  this  way  it  can  cross  holes  and  trenches  which 
would  stop  a  vehicle  with  wheels. 

the  change  ;  that  is,  energy  is  the  universal  agency  by  means 
of  which  work  is  done.  Water  in  an  elevated  reservoir, 
steam  under  pressure  in  a  boiler,  a  flying  shell  with  its 
content  of  explosives,  —  all  these  may  do  work,  may  over- 
come resistance,  or  change  the  position  or  motion  of  other 
bodies.  They  possess  energy  which  is  transferred  from 
them  to  the  bodies  on  which  work  is  done. 

2.  The  Universal  Science.  —  Since  everything  which  we 
recognize  by  the  senses  is  matter,  and  every  change  in 


THE   UNIVERSAL   SCIENCE  3 

matter  involves  energy,  it  is  plain  that  physics  is  a  uni- 
versal science,  touching  our  life  at  every  point.  Count- 
less physical  phenomena  are  taking  place  about  us  every 
day ;  a  girl  cooking,  a  boy  playing  ball,  the  fire-whistle 
blowing,  the  sun  giving  light  and  heat,  a  flag  flapping  in 
the  wind,  an  airplane  soaring  aloft,  an  apple  falling  from 


A  WRIGHT-MARTIN  "  BOMBER." 

An  airplane  which  can  cross  the  United  States  from  coast  to  coast  with 
only  one  stop. 

a  tree,  a  train  or  motor  car  whizzing  by,  a  British  "  tank  " 
crossing  a  shell-hole,  —  all  are  examples  of  matter  and 
associated  energy. 

Physics  is  not  so  much  concerned  with  matter  alone  or  with 
energy  alone  as  with  the  relations  of  the  two.  A  baseball  is  of  little 
interest  in  itself ;  it  becomes  interesting  only  in  connection  with  a 
bat  and  the  energy  of  the  player's  arm.  The  engine  driver's  inter- 
est is  not  so  much  in  the  engine  itself  as  in  the  engine  with  steam 
up  ready  to  drive  it.  No  one  would  care  to  buy  an  automobile  to 


4  INTRODUCTION 

stand  in  a  garage ;  its  attractiveness  lies  in  the  fact  that  it  becomes 
a  thing  of  life  when  its  motor  is  vitalized  by  the  heat  of  combustion 
of  gasoline  vapor. 

3.  Applications  of  the  Principles  of  Physics.  —  The  appli- 
cations  of   the   principles   of    physics   in    the   household 
and  in  the  familiar  arts  are  very  numerous  and  affect  us 
constantly  in  daily  life.     Water  under  pressure  is  deliv- 
ered for  domestic  use,  and  fuel  is  used  in  the  liquid  or 
in  the  gaseous  form  as  well  as  in  the  solid.     Electricity 
lights  our  houses,  toasts  our  bread,  and  even  cooks  our 
daily  food.     The  electric  motor  runs  our  vacuum  cleaners 
and  our  sewing  machines. 

The  applications  of  physics  in  modern  life  are  so  nu- 
merous and  they  are  changing  so  rapidly  that  we  cannot 
expect  to  learn  about  all  of  them  in  a  year's  study ;  but 
physical  principles  remain  the  same ;  and  if  we  acquire  a 
knowledge  of  these  principles  and  of  their  familiar  appli- 
cations, we  shall  be  prepared  to  understand  and  to  ex- 
plain other  applications  that  have  been  made  possible  by 
the  science  of  physics. 

So  this  book  lays  emphasis  on  the  underlying  princi- 
ples of  physics,  illustrating  them  by  some  of  their  inter- 
esting applications,  leaving  it  to  the  enthusiasm  and 
ingenuity  of  both  teacher  and  pupils  to  supplement  the 
applications  with  others  drawn  from  life  and  from  scien- 
tific journals. 

4.  States  of   Matter.  —  Matter  exists  in    three   distinct 
states,  exemplified   by  water,  which    may  assume   either 
the  solid,  the  liquid,  or  the  gaseous  form,  as  ice,  water,  or 
water  vapor. 

Briefly  described, 

Solids  have  definite  size  and  shape,  and  offer  resistance 
to  any  change  of  these. 


FORCE 


Liquids  have  definite  size,  but  they  take  the  shape  of  the 
container  and  have  a  free  surface. 

G-ases  have  neither  definite  size  nor  shape,  both  depending 
on  the  container. 

These  are  not  all  the  differences  between  solids,  liquids, 
and  gases,  but  they  serve  to  distinguish  between  them. 

Some  substances  are  neither  wholly  in  the  one  state  nor  in  the 
other.  Sealing  wax  softens  by  heat  and  passes  gradually  from  the 
solid  to  the  liquid  state.  Shoemaker's  wax  breaks  into  fragments  like 
a  solid  under  the  blow  of  a  hammer,  but  under  long-continued  pres- 
sure it  flows  like  a  liquid,  though  slowly,  and  it  may  be  molded  at  will. 

5.  Force.  —  Our  primitive  idea  of  force  is  that  of  a 
push  or  a  pull ;  it  is  derived  from  experience  in  making 
muscular  exertion  to 
move  bodies  or  to 
stop  their  motion. 
Pushing  a  chair, 
throwing  a  stone, 
pulling  a  cart,  row- 
ing a  boat,'  stretch- 
ing a  rubber  band, 
bending  a  bow, 
catching  a  ball,  lift- 
ing a  book,  —  all  re- 
quire muscular  ef- 
fort in  the  nature 
of  a  push  or  a  pull. 
Thus  force  implies  A  TRIP  HAMMER- 

a     push    or    a     pull      This  wei§hs  several  tons  and  will  exert  an 
, ,  '    *  enormous  force  on  the  red-hot  iron  below  it. 

though    not    neces- 
sarily muscular;  and  the  effect  of  the  action  of  a  force 
on  a  body  free  to  move  is  to  give  it  motion  or  to  change 


6  INTRODUCTION 

its  motion.  For  the  present  we  shall  make  use  of  the 
units  of  force  familiar  to  us,  such  as  the  pound  of  force 
and  the  gram  of  force,  meaning  thereby  the  forces  equal 
to  that  required  to  lift  the  mass  of  a  pound  and  that  of  a 
gram  respectively. 

II.  PROPERTIES  OF  MATTER 

6.  The  Properties  of  Matter  are  those  qualities  that  serve 
to  define  it,  as  well  as  to  distinguish  one  substance  from 
another.     All  matter  has  extension  or  occupies  space,  and 
so  extension  is  a  general  property  of  matter.     On  the  other 
hand  common  window  glass  lets  light  pass  through  it,  or  is 
transparent,    while  a  piece  of  sheet  iron  does  not  transmit 
light,  or  is  opaque.     A  watch  spring  recovers  its  shape 
after  bending,  or  is  elastic,  while  a  strip  of  lead  possesses 
this  property  in  so  slight  a  degree  that  it  is  classed  as  in- 
elastic.    So  we  see  that  transparency  and  elasticity  are 
special  properties  of  matter. 

7.  Extension.  —  All  bodies  have  three  dimensions,  length, 
breadth,  and  thickness.     A  sheet  of  tissue  paper  or  of  gold 
leaf,  at  first  thought,  appears  to  have  but  two  dimensions, 
length  and  breadth;  but  while  its  third  dimension  is  rel- 
atively small,  if  its  thickness  should  actually  become  zero, 
it  would  cea,se  to  be  either  a  sheet  of  paper  or  a  piece  of 
gold  leaf.     Extension  is  the  property  of  occupying  space  or 
having  dimensions. 

8.  Impenetrability.  —  While  matter  occupies  space,  no 
two  portions  of  matter  can  occupy  the  same  space  at  the 
same  time.     The  volume  or  bulk  of  an  irregular  solid,  such 
as  a  lump  of  coal,  may  be  measured  by  noting  the  volume  of 
liquid  displaced  when  the  solid  is  completely  immersed  in  it. 
The  general  property  of  matter  that  no  two  bodies  can  occupy 
the  same  space  at  the  same  time  is  known  as  impenetrability. 


INERTIA 

Put  a  lump  of  coal  into  a  tall  graduate 
partly  filled  with  water,  as  in  Fig.  1.  Note 
the  reading  at  the  surface  of  the  water  be- 
fore and  after  putting  in  the  coal ;  the  differ- 
ence is  the  volume  of  water  displaced,  or  the 
volume  of  the  piece  of  coal. 


9.  Inertia. —  The  most  conspicuous 
and  characteristic  general  property  of 
matter  is  inertia.  Inertia  is  the  prop- 
erty which  all  matter  possesses  of  resist- 
ing any  attempt  to  start  it  if  at  rest,  to 
stop  it  if  in  motion,  or  to  change  either  FIGURE  1.  — MEASURING 
the  direction  or  the  amount  of  its  motion.  VOLUME  BY  DlSPLACEMENT- 

If  a  moving  body  stops,  its 
arrest  is  always  owing  to 
something  outside  of  itself ; 
and  if  a  body  at  rest  is  set 
moving,  motion  must  be  given 
to  it  by  some  other  body.  It 
is  a  familiar  fact  that  no  body 
of  any  sort  will  either  start 
or  stop  moving  of  itself. 

10.  Illustrations  of  Inertia-  — 

Many  familiar  facts  are  due  to 
inertia.  When  a  street  car  stops 
suddenly,  a  person  standing  con~ 
tinues  by  inertia  to  move  forward, 
or  is  apparently  thrown  toward  the 
front  of  the  car ;  the  driver  of  a 
racing  motor  car  is  apparently 
thrown  with  violence  when  the 
rapidly  moving  car  collides  with  a 
post  or  a  tree ;  the  fact  is  the  car  is 
violently  stopped,  while  the  driver 
continues  to  move  forward  as  be- 


FIGURE  2.  —  STATUE   TWISTED 
AROUND  BY  EARTHQUAKE. 


8 


INTRODUCTION 


fore  the  collision.  When  a  fireman 
shovels  coal  into  a  furnace,  he  suddenly 
arrests  the  motion  of  the  shovel  and 
leaves  the  coal  to  move  forward  by 
inertia.  A  smooth  cloth  may  be 
snatched  from  under  a  heavy  dish  with- 
out disturbing  it.  The  violent  jar  to  a 
water  pipe  when  a  faucet  is  quickly 
closed  is  accounted  for  by  the  inertia 
of  the  stream.  Tall  columns,  chimneys, 
and  monuments  are  sometimes  twisted 
around  by  violent  earthquake  move- 
ments (Fig.  2).  The  sudden  circular 
motion  of  the  earth  under  a  column 
leaves  it  standing  still,  while  the  slower 
return  motion  carries  it  around.  The 
persistence  with  which  a  spinning  top 
maintains  its  axis  of  rotation  in  the  same 
direction  is  due  to  its  inertia.  If  it  is 
spun  on  a  smooth  surface,  like  a  mirror, 
and  is  tossed  into  the  air,  it  will  not 

tumble  over  and  over,  but  will  keep  upright  (Fig.  3)  and  may  be 

caught  on  the  mirror,  still  spin- 
ning on  its  point.     The  gyrostat 

wheel  acts  on  the  same  principle, 

and  so  does   Sperry's  gyrostatic 

compass    and    his   stabilizer  for 

ships  and  aeroplanes. 

If  a  round  flat  biscuit  is  pitched 

into  the  air,  there  is  no  certainty 

as  to  how  it  will  come  down ;  but 

if  it  is  given   a  spin  before  it 

leaves  the  hand,  the  axis  of  spin- 
ning keeps  parallel  to  itself  (Fig. 

4).    If  one  wants  to  throw  a  hoop 

or  a  hat  to  some  one  to  catch  on 

a  stick,  one  gives  to  the  hoop  or 

the  hat  a  spin.     So  also  if  one 

wants  to  throw  a  quoit  and  be 


FIGURE  3.  —  SPINNING 
MAINTAINS  ITS  Axis  OF 
TATION. 


TOP 
Ro- 


FIGURE  4.  —  SPINNING  BISCUIT. 


MA88  9 

certain  how  it  will  alight,  one  gives  it  a  spin.    Its  inertia  keeps  it 
spinning  around  the  same  axis  in  space. 

Tie  a  piece  of  twine  to  a  heavy  weight,  such  as  a  flatiron.  By  pull- 
ing slowly  the  flatiron  may  be  lifted,  but  a  sudden  jerk  on  the  twine 
will  break  it  because  of  the  inertia  of  the  weight. 

Suspend  a  heavy  weight  by  a  cotton  string,  as  in 
Fig.  5,  and  tie  a  piece  of  the  same  string  to  the 
under  side  of  the  weight.  A  steady  downward  pull 
at  B  will  break  the  upper  string  because  it  carries  the 
greater  load.  A  sudden  downward  pull  on  B  will 
break  the  lower  string  before  the  pull  reaches  the 
upper  one  on  account  of  the  inertia  of  the  weight. 

11.  Mass.  —  We  are  all  familiar  with  the 
fact  that  the  less  matter  there  is  in  a  body, 
the  more  easily  it  is  moved,  and  the  more  FIGURE  5.  - 

.,       .,    .  11-  /•  ^         INERTIA  EXPERI- 

easily  it  is  stopped  when  in  motion.     One 


MENT. 


can  tell  an  empty  barrel  from  a  full  one  by  a 
kick,  a  block  of  wood  from  a  brick  by  shoving  it  with  the 
foot,  and  a  tennis  ball  from  a  baseball  by  catching  it. 
The  mass  of  a  body  is  the  quantity  of  matter  it  contains  ; 
but  since  the  inertia  of  a  body  is  proportional  to  the 
quantity  of  matter  in  it,  it  is  not  difficult  to  see  that  the 
mass  of  a  body  is  the  measure  of  its  inertia. 

While  mass  is  most  easily  measured  by  means  of  weigh- 
ing, it  must  not  be  confused  with  weight  (§  132),  because 
mass  is  independent  of  the  earth-pull  or  gravity.  The 
mass  of  a  meteoric  body  is  the  same  when  flying  through 
space  as  when  it  strikes  the  earth  and  embeds  itself  in  the 
ground.  If  it  could  reach  the  center  of  the  earth,  its 
weight  would  become  zero;  at  the  surface  of  the  sun  it 
would  weigh  nearly  twenty-eight  times  as  much  as  at  the 
earth's  surface;  but  its  mass  would  be  the  same  every- 
where. For  this  reason,  and  others  which  will  appear 
later,  in  discussing  the  laws  of  physics  we  prefer  to  speak 


10 


INTRODUCTION 


of  mass  when  a  student  thinks  the  term  weight  might  be 
used  as  well. 

12.    Cohesion  and  Adhesion.  —  All  bodies  are  made  up  of 
very  minute  particles,  which  are  separately  invisible,  and 

are  called  mole- 
cules. Cohesion 
is  the  force  of  at- 
traction between 
molecules,  and  it 
binds  together 
the  molecules  of 
a  substance  so  as 
to  form  a  larger 
mass  than  a  mol- 
ecule. Adhe- 
sion is  the  force 
uniting  bodies  by 
their  adjacent 
surfaces.  When 
two  clean  sur- 
faces of  white- 
hot  wrought 
iron  are  brought 
into  close  con- 
tact by  hammer- 
ing, they  cohere 
and  become  a 
single  body.  If 
a  clean  glass  rod 
be  dipped  into  water  and  then  withdrawn,  a  drop  will  ad- 
here to  it.  Glue,  adhesive  plaster,  and  postage  stamps 
stick  by  adhesion.  Mortar  adheres  to  bricks  and  nickel 
plating  to  iron. 


COHESION. 

Mr.  Lambirth,  dean  of  blacksmiths  in  America, 
has  spent  35  years  at  the  head  of  the  forge  work  at 
the  Massachusetts  Institute  of  Technology. 


POROSITY 


11 


Suspend  from  one  of  the  arras  of  a  beam  balance  a  clean  glass  disk 
by  means  of  threads  cemented  to  it  (Fig.  6).     After  counterpoising 
the  disk,  place  below  it  a  vessel  of  water,  and  adjust  so  that  the  disk 
just  touches  the  surface  of  the  water  when  the  beam  of  the  balance  is 
horizontal.     Now  add  weights  to  the  opposite  pan  until  the  disk  is 
pulled  away  from  the  water.     Note  that  the  under  surface  of  the  disk 
is  wet.     The  adhesion  of  the 
water  to  the  glass  is  greater 
than  the   cohesion   between 
the  molecules  of  the  water. 
If    lycopodium    powder    be 
carefully  sifted  on  the  sur- 
face of  the  water,  the  water 
will   not   wet  the  disk   and 
there  will   be  no   adhesion. 
If  mercury  be  substituted  for 
water,  a  much  greater  force 
will  be  necessary  to  separate 
the  disk  from  the  mercury, 
but  no  mercury  will  adhere 
to  it.     The  force  of  cohesion 
between  the  molecules  of  the 
mercury  is  greater  than  the   adhesion  between   it   and  the  glass. 

Cut  a  fresh,  smooth  surface  on  each  of  two  lead  bullets  and  hold 
these  surfaces  gently  together.  They  will  not  stick.  Now  press  them 
tightly  together  with  a  slight  twisting  motion.  They  will  adhere 
quite  firmly.  This  fact  shows  that  molecular  forces  act  only  through 
insensible  distances.  It  has  been  shown  that  they  vanish  in  water  at 
a  range  of  about  one  five-hundred-thousandth  of  an  inch. 

An  interesting  example  of  selective  adhesion  occurs  in  the  winning 
of  diamonds  in  south  Africa.  The  mixed  pebbles  and  other  worthless 
stones,  with  an  occasionaUdiamond,  are  washed  down  an  inclined 
shaking  surface  covered  with  grease.  Only  the  diamonds  and  a  few 
other  precious  stones  stick  to  the  grease ;  the  rest  are  washed  away. 

13.  Porosity.  —  Sandstone,  unglazed  pottery,  and  similar 
bodies  absorb  water  without  change  in  volume.  The  water 
fills  the  small  spaces  called  pores,  which  are  visible  either 
to  the  naked  eye  or  under  a  microscope.  All  matter  is 


FIGURE  6.  —  GLASS  ADHERES  TO  WATER. 


12  INTRODUCTION 

probably  porous,  though  the  pores  are  invisible,  and  the 
corresponding  property  is  called  porosity.  In  a  famous 
experiment  in  Florence  many  years  ago,  a  hollow  sphere 
of  heavily  gilded  silver  was  filled  with  water  and  put 
under  pressure.  The  water  came  through  the  pores  of  the 
silver  and  gold  and  stood  in  beads  on  the  surface.  Francis 
Bacon  observed  a  similar  phenomenon  with  a  lead  sphere. 

Oil  penetrates  into  marble  and  spreads  through  it.  Even  so  dense 
a  substance  as  agate  is  porous,  for  it  is  artificially  colored  by  the  ab- 
sorption, first  of  one  liquid  and  then  of  another  which  acts  chemically 
on  the  first ;  the  result  is  a  deposit  of  coloring  matter  in  the  pores  of 
the  agate. 

14.  Tenacity  and  Tensile  Strength.  —  Tenacity  is  the  resist- 
ance which  a  body  offers  to  being  torn  apart.     The  tensile 

strength  of  wires  is  tested  by  hanging  them 
vertically  and  loading  with  successive  weights 
until  they  break  (Fig.  7).  The  breaking 
weights  for  wires  of  different  materials  but  of 
the  same  cross  section  differ  greatly.  A  knowl- 
edge of  tensile  strength  is  essential  in  the  de- 
sign of  telegraph  wires  and  cables,  suspension 
bridges,  and  the  tension  members  of  all  steel 
structures. 

Tenacity  diminishes  with  the  duration  of  the 
pull,  so  that  wires  sometimes  break  with  a  load 
which  they  have  supported  for  a  long  time. 

Lead  has  the  least  tenacit7  of  a11  solid  metals, 
STRENGTH  and  cast  steel  the  greatest.  Even  the  latter  is 
OF  WIRE.  exceeded  by  fibers  of  silk  and  cotton.  Single 
fibers  of  cotton  can  support  millions  of  times  their  own 
weight. 

15.  Ductility. — Ductility  is  the  property  of  a  substance 
which  permits  it  to  be  drawn  into  wires  or  filaments.     Gold,' 


TENACITY  AND   TENSILE  STRENGTH 


13 


copper,  silver,  and  platinum  are  highly  ductile.  The  last 
is  the  most  ductile  of  all.  It  has  been  drawn  into  wire 
only  0.00003  inch  in  diameter.  A  mile  of  this  wire  would 
weigh  only  1.25  grains. 


AERIAL  TRAMWAY  OVER  THE  WHIRLPOOL  RAPIDS. 
The  cables  have  great  tensile  strength  to  support  the  car. 

Other  substances  are  highly  ductile  only  at  high  tem- 
peratures. Glass  has  been  spun  into  such  fine  threads 
that  a  mile  of  it  would  weigh  only  one  third  of  a  grain. 
Melted  quartz  has  been  drawn  into  threads  not  more  than 
0.00001  inch  in  diameter.  Such  threads  have  nearly  as 
great  tenacity  as  steel. 


14 


INTRODUCTION 


16.    Malleability.  —  Malleability  is  a  property  which  per- 
mits  of  hammering  or  rolling  some  metals  into  thin  sheets. 

Gold  leaf,  made  by 
hammering  between 
skins,  is  so  thin  that 
it  is  partially  trans- 
parent and  trans- 
mits green  light. 
Zinc  is  malleable 
when  heated  to  a 
temperature  of  from 
100°  to  150°  C. 
(centigrade  scale). 
It  can  then  be  rolled 
into  sheets.  Nickel 
at  red  heat  can 
be  worked  like 
wrought  iron.  Mal- 
leable iron  is  made 
from  cast  iron  by 
heating  it  for  sev- 
eral days  in  contact  with  a  substance  which  removes  some 
of  the  carbon  from  the  cast  iron. 

17.  Hardness  and  Brittleness.  —  Hardness  is  the  resistance 
offered  by  a  body  to  scratching  by  other  bodies.  The  relative 
hardness  of  two  bodies  is  ascertained  by  finding  which  will 
scratch  the  other.  Diamond  is  the  hardest  of  all  bodies 
because  it  scratches  all  others.  Sir  William  Crookes  has 
shown  that  diamonds  under  great  hydraulic  pressure  be- 
tween mild  steel  plates  completely  embed  themselves  in 
the  metal.  Carborundum,  an  artificial  material  used  for 
grinding  metals,  is  nearly  as  hard  as  diamond. 

Brittleness  is  aptness  to  break  under  a  blow.     It  must  be 


POURING  MOLTEN  IRON  INTO  MOULDS. 


HARDNESS  AND  BRITTLENESS  15 

distinguished  from  hardness.     Steel  is  hard  and  tough, 
while  glass  is  hard  and  brittle. 

Tool  steel  becomes  glass-hard  and  brittle  when  suddenly 
cooled  from  a  high  temperature.  The  tempering  of  steel 
is  the  process  of  giving  the  degree  of  hardness  required 
for  various  purposes.  It  consists  usually  in  first  plunging 
the  article  at  red  heat  into  cold  water  or  other  liquid  to 
give  it  an  excess  of  hardness  ;  then  reheating  gradually 
until  the  hardness  is  reduced,  or  "  drawn  down,"  to  the 
required  degree.  The  indication  of  the  hardness  is  the 
color  appearing  on  a  polished  portion,  such  as  straw- 
yellow,  brown-yellow,  purple,  or  blue. 

The  process  of  annealing  as  applied  to  iron  and  glass  is  used  to 
render  them  less  brittle.  It  is  done  by  cooling  very  slowly  and  uni- 
formly from  a  high  temperature.  Soft  iron  is  thus  made  more  ductile, 
while  glass  is  relieved  from  the  molecular  stresses  set  up  in  rapid 
cooling,  and  it  thus  becomes  tougher  and  more  uniform.  The  best 
lamp  chimneys  are  annealed  by  the  manufacturer.  Disks  of  glass  for 
telescope  lenses  and  mirrors  must  be  carefully  annealed  to  prevent 
fracture  and  warping  during  the  process  of  grinding  and  polishing. 

Prince  Rupert  drops  (Fig.  8)  are  made  by  dropping  melted  glass 
into  cold  water.  The  outside  is  suddenly  chilled  and  solidified,  while 
the  interior  is  still  fused,  and  when  it  cools  it  must  ac- 
commodate itself  to  the  dimensions  of  the  outer  skin. 
The  drop  is  thus  under  great  tension.  With  a  pair 
of  pliers  break  off  the  tip  of  the  drop  under  water 
in  a  tumbler,  or  scratch  with  a  file  ;  the  whole  drop 
will  fly  to  powder  with  almost  explosive  violence. 


A  large  tall  jar  on  foot  is  usually  thick  at  the  bot-  : 


torn,  and  imperfectly  annealed.  Such  jars  have  not 
infrequently  been  broken  by  a  scratch  inside,  made,  for  example,  by 
stirring  emery  powder  in  water  by  means  of  a  long  wooden  stick. 
A  scratch  inside  is  usually  fatal  to  a  lamp  chimney. 

A  large  glass  tube  may  be  cut  in  two  by  scratching  it  around  on  the 
inside  by  means  of  an  appropriate  tool,  and  then  carefully  heating  it 
in  a  small  gas  flame. 


16  INTRODUCTION 

Exercises 

1.  Given  a  large  crystal  of  rock  candy.     Can  its  volume  be  deter- 
mined by  the  method  outlined  under  impenetrability  ?     How  ? 

2.  The  volume  of  a  bar  of  lead  can  be  reduced  by  pounding  it. 
Explain. 

3.  A  small  quantity  of  sugar  can  be  dissolved  in  a  cup  of  water 
without  increasing  the  volume.     Explain. 

4.  A  quick  blow  with  a  heavy  knife  will  often  remove  smoothly 
the  neck  of  a  glass  bottle,  while  a  less  vigorous  blow  will  shatter  the 
bottle.     Explain. 

5.  Why  can  an  athlete  jump  farther  in  a  running  jump  than  in 
a  standing  jump  ? 

6.  By  striking  the  end  of  the  handle  it  can  be  driven  into  a  heavy 
ax  much  better  than  by  pounding  the  ax.     Why  ? 

7.  A  man  standing  on  a  flat-bottomed  car  that  is  moving  jumps 
'vertically  upward.     Will  he  come  down  on  the  spot  from  which  he 
jumped  ?     Explain. 

8.  If  a  top  be  set  spinning  it  stands  up  ;  if  not  spinning  it  topples 
over.     Explain. 

9.  A  bullet  fired  from  a  rifle  will  pass  through  a  pane  of  glass, 
cutting  a  fairly  smooth  hole  ;  a  stone  thrown  by  the  hand  on  striking 
a  pane  of  glass  will  shatter  it.     Explain. 

10.  Name  three  properties  of  matter  that  are  characteristic  of  it. 

11.  A  rolling  wheel  does  not  fall  over,  but  one  not  rolling  topples 
over.     Why  ? 

12.  Why  hold  a  heavy  hammer  against  a  spring  board  when  driv- 
ing a  nail  into  it? 

13.  In  Jules  Verne's  Trip  to  the  Moon  the  incident  is  told  that 
when  a  few  days  on  the  way  the  dog  died  and  was  thrown  overboard. 
To  their  surprise  the  dead  dog  followed  along  after  them.    Is  Verne's 
Physics  correct  ?     Explain. 

II.     PHYSICAL  MEASUREMENTS 

18.  Units.  —  To  measure  any  physical  quantity  a  certain 
definite  amount  of  the  same  kind  of  quantity  is  used  as  the 
unit.  For  example,  to  measure  the  length  of  a  body,  some 


MEASURES   OF  LENGTH  17 

arbitrary  length,  as  a  foot,  is  chosen  as  the  unit  of  length; 
the  length  of  a  body  is  the  number  of  times  this  unit  is  con- 
tained in  the  longest  dimension  of  the  body.  The  unit  is 
always  expressed  in  giving  the  magnitude  of  any  physical 
quantity;  the  other  part  of  the  expression  is  the  numerical 
value.  For  example,  60  feet,  500  pounds,  45  seconds. 

In  like  manner,  to  measure  a  surface,  the  unit,  or  stand- 
ard surface,  must  be  given,  such  as  a  square  foot;  and  to 
measure  a  volume,  the  unit  must  be  a  given  volume,  such, 
for  example,  as  a  cubic  inch,  a  quart,  or  a  gallon. 

19.  Systems  of  Measurement.  —  Commercial  transactions  in 
most  civilized  countries  are  carried  on  by  a  decimal  system 
of  money,  in  which  all  the  multiples  are  ten.     It  has  the 
advantage  of  great  convenience,  for  all  numerical  operations 
in  it  are  the  same  as  those  for  abstract  numbers  in  the  dec- 
imal system.     The  system  of  weights  and  measures  in  use 
in  the  British  Isles  and  in  the  United  States  is  not  a  dec- 
imal system,  and  is  neither  rational  nor  convenient.     On 
the  other  hand  most  of  the  other  civilized  nations  of  the 
world  within  the  last  fifty  years  have  adopted  the  metric 
system,  in  which  the  relations  are  all  expressed  by  some 
power  of  ten.     The  metric  system  is  in  well-nigh  universal 
use  for  scientific  purposes.     It  furnishes  a  common  numer- 
ical language  and  greatly  reduces  the  labor  of  computation. 

20.  Measures  of  Length.  —  In  the  metric  system  the  unit 
of  length  is  the  meter.     In  the  United  States  it  is  the  dis- 
tance between  two  transverse  lines  on  each  of  two  bars  of 
platinum-iridium  at  the  temperature  of  melting  ice.     These 
bars,  which  are  called  "national  prototypes,"  were  made 
by  an  international  commission  and  were  selected  by  lot 
after  two  others  had  been  chosen  as  the  "  international  pro- 
totypes "  for  preservation  in  the  international  laboratory 
on  neutral   ground  at  Sevres  near  Paris.     Our   national 


18 


INTRODUCTION 


prototypes  are  preserved  at  the  Bureau  of  Standards  in 
Washington.  Figure  9  shows  the  two  ends  of  one  of 
them.  The  only  multiple  of  the  meter  in  general  use  is  the 
kilometer,  equal  to  1000  meters.  It  is  used  to  measure  such 
distances  as  are  expressed  in  miles  in  the  English  system. 


FIGURE  9.  —  ENDS  OF  METER  BAR. 

The  Common  Units  in  the  Metric  System  are : 

1  kilometer  (km.)  =  1000  meters  (m.) 

1  meter  =  100  centimeters  (cm.) 

1  centimeter  =10  millimeters  (mm.) 

The  Common  Units  in  the  English  System  are: 

1  mile  (mi.)  =  5280  feet  (ft.) 

1  yard  (yd.)  =  3  feet 

1  foot  =  12  inches  (in.) 

By  Act  of  Congress  in  1866  the  legal  value  of  the  yard 
is  fffy  meter;  conversely  the  meter  is  equal  to  39.37 
inches.  The  inch  is,  therefore,  equal  to  2.540  centimeters. 

100  MILLIMETERS  =  10  CENTIMETERS  =  1  DECIMETER  =  3. 937  INCHES. 


INCHES  AND  TENTHS 

FIGURE  10.  —  CENTIMETER  AND  INCH  SCALES. 

The  unit  of  length  in  the  English  system  for  the  United 
States  is  the  yard,  defined  as  above.  The  relation  between 
the  centimeter  scale  and  the  inch  scale  is  shown  in  Fig.  10. 


CUBIC  MEASURE 


19 


Square  Inch 


21.  Measures  of  Surface.  —  In  the  metric  system  the  unit 
of  area  used  in  the  laboratory  is  the  square  centimeter 
(cm.2).  It  is  the  area  of  a  square,  the  edge  of  which  is 
one  centimeter.  The  square  meter  (m.2)  is  often  em- 
ployed as  a  larger  unit  of  area.  In  the 
English  system  both  the  square  inch 
and  the  square  foot  are  in  common  use. 
Small  areas  are  measured  in  square 
inches,  while  the  area  of  a  floor  and 
that  of  a  house  lot  are  given  in 
square  feet;  larger  land  areas  are  in 
acres,  640  of  which  are  contained  in  a 
square  mile. 

The  square  inch  contains  2.54  x  2.54 
=  6.4516  square  centimeters.     The  relative  sizes  of  the 
two  are  shown  in  Fig.  11. 

The  area  of  regular  geometric  figures  is  obtained  by  computation 
from  their  linear  dimensions.  Thus  the  area  of  a  rectangle  or  of  a 
parallelogram  is  equal  to  the  product  of  its 
base  and  its  altitude  (A  =  b  x  h) ;  the  area 
of  a  triangle  is  half  the  product  of  its  base 
and  its  altitude  (A  =^b  x  h)  ;  the  area  of  a 
circle  is  the  product  of  3.1416  (very  nearly 
%p)  and  the  square  of  the  radius  (A  —  irr  2)  ; 
the  surface  of  a  sphere  is  four  times  the  area 
of  a  circle  through  its  center  (A  =  4ur2). 
For  other  surfaces,  see  Appendix  III. 


FIGURE  11.  — 
SQUARE  CENTIMETER 
AND  SQUARE  INCH. 


FIGURE  12.  —  CUBIC 
CENTIMETER  AND  CUBIC 
INCH. 


22.  Cubic  Measure.  —  The  smaller 
unit  of  volume  in  the  metric  system 
is  the  cubic  centimeter.  It  is  the  vol- 
ume of  a  cube,  the  edges  of  which  are 
one  centimeter  long.  The  cubic  inch  equals  (2.54)8  or 
16.387  cubic  centimeters.  The  relative'  sizes  of  the  two 
units  are  shown  in  Fig.  12.  In  the  English  system  the 


20 


INTRODUCTION 


Cm  .3 
15°C. 
-500 


FIGURE  13. 
—  CYLINDRI- 
CA L  GLASS 
GRADUATE. 


cubic  foot  and  cubic  yard  are  employed  foi 
larger  volumes.  The  cubical  capacity  of  a 
room  or  of  a  freight  car  would  be  expressed 
in  cubic  feet ;  the  volume  of  building  sand 
and  gravel  or  of  earth  embankments,  cuts, 
or  fills  would  be  in  cubic  yards. 

The  unit  of  capacity  for  liquids  in  the 
metric  system  is  the  liter.  It  is  a  decimeter 
cube,  that  is,  1000  cubic  centimeters.  The 
imperial  gallon  of  Great  Britain  contains 
about  277.3  cubic  inches,  and  holds  10 
pounds  of  water  at  a  temperature  of  62° 
Fahrenheit.  The  United  States  gallon  has 
the  capacity  of  231  cubic  inches. 

Common  Units  in  the  Metric  Sys- 
tem : 


1  cubic  meter  (m.3)    =  1000  liters  (1.) 

1  liter  =  1000  cubic  centimeters  (crn.3) 

Common  Units  in  the  English  System : 

1  cubic  yard  (cu.yd.)=  27  cubic  feet  (cu.  ft.) 

1  cubic  foot  =  1728  cubic  inches  (cu.  in.) 

1  U.  S.  gallon  (gal.)  =  4  quarts  (qt.)  =  231  cubic  inches 

1  quart  =  2  pints  (pt.) 

The  volume  of  a  regular  solid,  or  of  a  solid  geometrical  figure,  may 
be  calculated  from  its  linear  dimensions.  Thus,  the  number  of  cubic 
feet  in  a  room  or  in  a  rectangular  block  of  marble  is  found  by  get- 
ting the  continued  product  of  its  length,  its  breadth,  and  its  height, 
all  measured  in  feet.  The  volume  of  a  cylinder  is  equal  to  the  product 
of  the  area  of  its  base  (Tir2)  and  its  height,  both  measured  in  the 
same  system  of  units. 

Liquids  are  measured  by  means  of  graduated  vessels  of  metal  or  of 
glass.  Thus,  tin  vessels  holding  a  gallon,  a  quart,  or  a  pint  are  used 


UNITS  OF  MASS 


21 


FIGURE  14. 
—  VOLUMETRIC 
FLASK. 


for  measuring  gasoline,  sirup,  etc.     Bottles  for  acids  usually  hold 
either  a  gallon  or  a  half  gallon,  and  milk  bottles  contain  a  quart,  a 
pint,  or  a  half  pint.     Glass  cylindrical  graduates  (Fig. 
13)  and  volumetric  flasks  (Fig.  14)  are  used  by  phar-  A 

macists,  chemists,  and  physicists  to  measure  liquids. 
In  the  metric  system  these  are  graduated  in  cubic  cen- 
timeters. 

23.  Units  of  Mass.  —  The  unit  of  mass  in 
the  metric  system  is  the  kilogram.  The 
United  States  has  two  prototype  kilograms 
made  of  platinum-iridium  and  preserved  at 
the  Bureau  of  Standards  in  Washington 
(Fig.  15).  The  gram  is  one  thousandth  of 
the  kilogram.  The  latter  was  originally  de- 
signed to  represent  the  mass  of  a  liter  of 
pure  water  at  4°  C.  (centigrade  scale).  For 
practical  purposes  this  is  the  kilogram.  The 
gram  is  therefore  equal  to  the  mass  of  a  cubic  centimeter 
of  water  at  the  same  temperature.  The  mass  of  a  given 

body  of  water  can 
thus  be  immediately 
inferred  from  its  vol- 
ume. 

The  unit  of  mass  in 
the  English  system  is 
the  avoirdupois  pound. 
The  ton  of  2000  pounds 
is  its  chief  multiple  ; 
its  submultiples  are  the 
ounce  and  the  grain. 
The  avoirdupois  pound 
is  equal  to  16  ounces 

FIGURE  15.  — STANDARD  KILOGRAM.  and     to     7000     grains. 


22  INTRODUCTION 

The  "  troy  pound  of  the  mint  "  contains  5760  grains.  In 
1866  the  mass  of  the  5-cent  nickel  piece  was  legally  fixed 
at  5  grams  ;  and  in  1873  that  of  the  silver  half  dollar  at 
12.5  grams.  One.  gram  is  equal  approximately  to  15.432 
grains.  A  kilogram  is  very  nearly  2.2  pounds.  More 
exactly,  one  kilogram  equals  2.20462  pounds. 

All  mail  matter  transported  between  the  United  States  and  the  fifty 
or  more  nations  signing  the  International  Postal  Convention,  including 
Great  Britain,  is  weighed  and  paid  for  entirely  by  metric  weight. 
The  single  rate  upon  international  letters  is  applied  to  the  standard 
weight  of  15  grams  or  fractional  part  of  it.  The  International  Parcels 
Post  limits  packages  to  5  kilograms;  hence  the  equivalent  limit  of 
11  pounds. 

Common  Units  in  the  English  System : 

1  ton  (T.)  =  2000  pounds  (Ib.) 
1  pound      =  16  ounces  (oz.) 
1  ounce       =  437.5  grains  (gr.) 

Common  Units  in  the  Metric  System  : 

1  kilogram  (kg.)  =  1000  grams  (g.) 

1  gram  =  1000  milligrams  (mg.) 

24.  The  Unit  of  Time.  —  The  unit  of  time  in  universal 
use  in  physics  and  by  the  people  is  the  second.  It  is 
.g-g-J^  of  a  mean  solar  day.  The  number  of  seconds  be- 
tween the  instant  when  the  sun's  center  crosses  the  me- 
ridian of  any  place  and  the  instant  of  its  next  passage 
over  the  same  meridian  is  not  uniform,  chiefly  because 
the  motion  of  the  earth  in  its  orbit  about  the  sun  varies 
from  day  to  day.  The  mean  solar  day  is  the  average 
length  of  all  the  variable  solar  days  throughout  the  year. 
It  is  divided  into  24  x  60  x  60  =  86,400  seconds  of  mean 
solar  time,  the  time  recorded  by  clocks  and  watches. 


PROBLEMS  23 

The  sidereal  day  used  in  astronomy  is  nearly  four  minutes 
shorter  than  the  mean  solar  day. 

25.  The  Three  Fundamental  Units.  —  Just  as  the  meas- 
urement of  areas  and  of  volumes  reduces  simply  to  the 
measurement  of  length,  so  it  has  been  found  that  the 
measurement  of  most  other  physical  quantities,  such  as 
the  speed  of  a  ship,  the  pressure  of  water  in  the  mains, 
the  energy  consumed  by  an  electric  lamp,  and  the  horse 
power  of  an  engine,  may  be  made  in  terms  of  the  units  of 
length,  mass,  and  time.  For  this  reason  these  three  are 
considered  fun  dam  ental  units  to  distinguish  them  from  all 
others,  which  are  called  derived  units. 

The  system  now  in  general  use  in  the  physical  sciences 
employs  the  centimeter  as  the  unit  of  length,  the  gram,  as 
the  unit  of  mass,  and  the  second  as  the  unit  of  time.  It 
is  accordingly  known  as  the  c.  g.  s.  (centimeter-gram- 
second)  system. 

Problems 

In  solving  these  problems  the  student  should  use  the  relations  and 
values  given  in  §§  20,  22,  and  23. 

1.  Reduce  76  cm.  to  its  equivalent  in  inches. 

2.  Express  in  feet  the  height  of  Eiffel  Tower,  355  m. 

3.  The  metric  ton  is  1000  kg.     Find  the  difference  between  it  and 
an  American  ton. 

4.  If  milk  is  15  cents  a  quart,  what  would  be  the  price  per  liter? 

5.  On  the  basis  that  one  liter  of  water  weighs  a  kilogram,  what 
would  a  gallon  of  water  weigh  in  pounds  ? 

6.  What  per  cent  larger  than   a  pound  avoirdupois  is   half   a 
kilogram  ? 

7.  If  the  speed  limit  on  a  state  road  is  25  mi.  per  hour,  what  would 
that  be  expressed  in  kilometers  per  hour  ? 

8.  How  many  liters  in  a  cubic  foot  of  water? 


24  IN  TR  OD  UCTION 

9.    What  is  the  equivalent  in  the  metric  system  of  a  velocity  of 
1090  ft.  per  second  ? 

10.  If  a  cylindrical  jar  is  4  in.  in  diameter  and  one  foot  deep,  how 
many  liters  will  it  hold  ? 

11.  Express  the  velocity  of  light,   186,000  miles  per  second,  in 
kilometers  per  second. 

12.  What  would  be  the  error  made  if  in  measuring  12  ft.  a  bar 
30  cm.  long  is  used  as  a  foot  ? 

13.  If  a  cubic  foot  of  water  weighs  62.4  lb.,  what  would  a  pint  of 
water  weigh? 

14.  If  coal  sells  at  $12  per  ton,  what  would  20,000  kilograms  cost? 


CHAPTER  II 


MOLECULAR  PHYSICS 
I.   MOLECULAR  MOTION 

26.  Diffusion  of  Gases.  —  If  two  gases  are  placed  in  free 
communication  with  each  other  and  are  left  undisturbed, 
they  will  mix  rather  rapidly.  Even  though  they  differ  in 
density  and  the  heavier  gas  is  at  the  bottom,  the  mixing 
goes  on.  This  process  of  the  spontaneous  mixing  of  gases 
is  called  diffusion. 

The  rapidity  with  which  gases  diffuse  may  be  illus- 
trated by  allowing  illuminating  gas  to  escape  into  a  room, 
or  by  exposing  ammonia  in  an  open  dish.  The  odor 
quickly  reveals  the  presence  of  either  gas  in  all  parts  of 
the  room,  even  when  air  currents  are  suppressed  as  far  as 
possible.  A  more  agreeable  illustration  is  furnished  by  a 
bottle  of  smelling  salts.  If  it  is  left 
open,  the  perfume  soon  pervades  the 
whole  room. 

Fill  one  of  a  pair  of  jars  (Fig.  16)  with  the 
fumes  of  strong  hydrochloric  acid,  and  the 
other  with  gaseous  ammonia,  and  place  over 
them  the  glass  covers.  Bring  the  jars  together 
as  shown,  and  after  a  few  seconds  slip  out  the 
cover  glasses.  In  a  few  minutes  both  jars  will 
be  filled  with  a  white  cloud  of  the  chloride  pIGURE  1 6.— DIFFUSION 
of  ammonia.  Instead  of  these  vapors,  air  and  OF  GASES 

illuminating  gas  may  be  used,  and  after  dif- 
fusion, the  presence  of  an  explosive  mixture  in  both  jars  may  be 
shown  by  applying  a  flame. to  the  mouth  of  each  separately. 

25 


MOLECULAR  PHYSICS 


27.  Effusion  through  Porous  Walls.  —  The  passage  of  a 
gas  through  the  pores  of  a  solid  is  known  as  effusion. 
The  rate  of  effusion  for  different  gases  is  nearly  inversely 
proportional  to  the  square  root  of  their 
relative  densities.  Hydrogen,  for  ex- 
ample, which  is  one  sixteenth  as  heavy  as 
oxygen,  passes  through  very  small  open- 
ings four  times  as  fast  as  oxygen. 

Cement  a  small  unglazed  battery  cup  to  a  funnel 
tube,  and  connect  the  latter  to  a  flask  nearly  filled 
with  water  and  fitted  with  a  jet  tube,  as  shown  in 
Fig.  17.  Invert  over  the  porous  cup  a  large  glass 
beaker  or  bell  jar,  and  pass  into  it  a  stream  of  hy- 
drogen or  illuminating  gas.  If  all  the  joints  are 
air-tight,  a  small  water  jet  will  issue  from  the  fine 
tube.  The  hydrogen  passes  freely  through  the  in- 
visible  pores  in  the  walls  of  the  porous  cup  and 
produces  gas  pressure  in  the  flask.  If  the  beaker 
is  now  removed,  the  jet  subsides  and  the  pressure 
in  the  flask  quickly  falls  to  that  of  the  air  outside 
by  the  passage  of  hydrogen  outward  through  the  pores  of  the  cup. 


FIGURE  17  _ 
EFFUSION  OF  HY- 
DROGEN. 


28.  Molecular  Motion  in  Gases.  —  The  simple  facts  of  the 
diffusion  and  effusion  of  gases  lead  to  the  conclusion  that 
their  molecules  (§12)  are  not  at  rest,  but  are  in  constant 
and  rapid  motion.  The  property  of  indefinite  expansibility 
is  a  further  evidence  of  molecular  motion  in  gases.  No 
matter  how  far  the  exhaustion  is  carried  by  an  air  pump, 
the  gas  remaining  in  a  closed  vessel  expands  and  fills  it. 
This  is  not  due  to  repulsion  between  the  molecules,  but 
to  their  motions.  Gases  move  into  a  good  vacuum  much 
more  quickly  than  they  diffuse  through  one  another.  In 
diffusion  their  motion  is  frequently  arrested  by  molecular 
collisions,  and  hence  diffusion  is  impeded. 

The  property  of  rapid  expansion  into  a  free  space  is  a 


THE   VELOCITY  OF  MOLECULES 


27 


highly  important  one.  The  operation  of  a  gasoline  engine, 
in  which  the  inlet  valve  presents  only  a  narrow  opening 
for  a  small  fraction  of  a  second,  is  an  excellent  illustration  ; 
and  yet  this  brief  period  suffices  for  the  explosive  mixture 
to  enter  and  fill  the 
cylinder 

29.  Pressure  Produced 
by  Molecular  Bombard- 
ment.—  It  would  be 
possible  to  keep  an  iron 
plate  suspended  hori- 
zontally in  the  air  by 
the  impact  of  a  great 
many  bullets  fired  up 
against  its  under  sur- 
face. The  clatter  of  an 
indefinitely  large  num- 
ber of  hailstones  on  a 
roof  forms  a  continuous 
sound,  and  their  fall 
beats  down  a  field  of 
grain  flat  to  the  ground. 
So  the  rapidly  moving 
molecules  of  a  gas  strike 


CROSS  SECTION  OF  AUTOMOBILE  MOTOR. 


The  valve  V  is  open  only  a  fraction  of  a 
second,  but  the  gas  fills  the  cylinder  C 
completely. 


innumerable  minute 
blows  against  the  walls 
of  the  containing  vessel,  and  these  blows  compose  a  con- 
tinuous pressure.  This,  in  brief,  is  the  kinetic  theory  of 
the  pressure  of  a  gas. 

30.  The  Velocity  of  Molecules.  —  It  has  been  found  pos- 
sible to  calculate  the  velocity  which  the  molecules  of  air 
must  have  under  standard  conditions  to  produce  by  their 
impact  against  the  walls  of  a  vessel  the  pressure  of  one 


28  MOLECULAR  PHYSICS 

atmosphere,  or  1033  g.  per  square  centimeter.  It  is  about 
450  m.  per  second.  For  the  same  pressure  of  hydrogen, 
which  is  only  one  fourteenth  as  heavy  as  air,  the  velocity 
has  the  enormous  value  of  1850  m.  per  second.  The  high 
speed  of  the  hydrogen  molecules  accounts  for  their  rela- 
tively rapid  progress  through  porous  walls. 

31.  Diffusion  of  Liquids.  —  Liquids  diffuse  into  one  an- 
other  in   a   manner   similar   to   that   of    gases,    but    the 

process  is  indefinitely  slower.  Diffusion  in 
liquids,  as  in  gases,  shows  that  the  molecules 
have  independent  motion  because  they  move 
more  or  less  freely  among  one  another. 

Let  a  tall  jar  be  nearly  filled  with  water  colored  with 
blue  litmus,  and  let  a  little  strong  sulphuric  acid  be  intro- 
duced into  the  jar  at  the  bottom  by  means  of  a  thistle  tube 
(Fig.  18).  The  density  of  the  acid  is  1.8  times  that  of  the 
litmus  solution,  and  the  acid  therefore  remains  at  the  bot- 
tom with  a  well-defined  surface  of  separation,  which  turns 
red  on  the  litmus  side  because  acid  reddens  litmus.  But 
if  the  jar  be  left  undisturbed  for  a  few  hours,  the  line  of 
separation  will  lose  its  sharpness  and  the  red  color  will 

move  gradually  upward,  showing  that  the  acid  molecules  have  made 

their  way  toward  the  top. 

32.  Diffusion  of  Solids.  —  The  diffusion  of  solids  is  much 
less  pronounced  than  the  diffusion  of  gases  and  liquids,  but 
it  is  known  to  occur.     Thus,  if  gold  be  overlaid  with  lead, 
the  presence  of  gold  throughout  the  lead  may  in  time  be 
detected.     Mercury  appears   to  diffuse   through  lead   at 
ordinary  temperatures ;    in    electroplating   the   deposited 
metal  diffuses  slightly  into   the  baser  metal ;    at   higher 
temperatures  metals  diffuse  into  one  another  to  a  marked 
degree,  so  that  there  is  evidence  of  molecular  motion  in 
solids  also. 


MOLECULAR  FORCES  IN  LIQUIDS 


29 


II.   SURFACE  PHENOMENA 

33.  Molecular  Forces  in  Liquids.  —  By  an  easy  transition 
of  ideas  we  carry  the  primitive  conception  of  force  derived 
from  the  sense  of  muscular  exertion  over  to  forces  other 
than  those  exerted  by  men  and  animals,  such  as  those  be- 
tween the  molecules  of  a  body.  Molecular  forces  act  only 
through  insensible  distances,  such  as  the  distances  separat- 
ing the  molecules  of  solids  and  liquids.  A  clean  glass 
rod  does  not  attract  water  until  there  is 
actual  contact  between  the  two.  If  the 
rod  touches  the  water,  the  latter  clings 
to  the  glass,  and  when  the  rod  is  with- 
drawn, a  drop  adheres  to  it.  If  the  drop 
is  large  enough,  its  weight  tears  it  away, 
and  it  falls  as  a  little  sphere. 

By  means  of  a  pipette  a  large  globule  of  olive 

oil   may  be  introduced  below   the  surface  of   a 

mixture  of  water  and  alcohol,  the  mixture  having 

been  adjusted  to  the  same  density  (§  69)  as  that  of  the  oil  by  varying 

the  proportions.     The  globule  then  assumes  a  truly  spherical  form  and 

floats  anywhere  in  the  mixture  (Fig.  19). 

Cover  a  smooth  board  with  fine  dust,  such  as  lycopodium  powder 

or  powdered  charcoal.     If  a  little  water  be  dropped  upon  it  from  a 

height  of  about  two 
feet,  it  will  scatter  and 
take  the  form  of  little 
spheres  (Fig.  20). 


FIGURE  1  9.— 

SPHERICAL  GLOBULE 
OF  OIL. 


FIGURE  20.  —  SPHERICAL  DROPS  OF  WATER. 


In  all  these  illus- 
trations the  spheri- 
cal form  is  ac- 
counted for  by  the  forces  between  the  molecules  of  the 
liquid.  They  produce  uniform  molecular  pressure  and 
form  little  spheres,  because  a  spherical  surface  is  the 
smallest  that  will  inclose  the  given  volume. 


MOLECULAR  PHYSICS 


FIGURE  21 .— 
NEEDLE  FLOATING  ON 
WATER. 


34.  Condition  at  the  Surface  of  a  Liquid.  —  Bubbles  of  gas  re- 
leased in  the  interior  of  a  cold  liquid  and  rising  to  the  surface  often 
show  some  difficulty  in  breaking  through.     A  sewing  needle  carefully 
placed  on  the  surface  of  water  floats.     The  water  around  the  needle  is 

depressed  and  the  needle  rests  in  a  little  hollow 
(Fig.  21). 

Let  two  bits  of  wood  float  on  water  a  few  mil- 
limeters apart.  If  a  drop  of  alcohol  is  let  fall  on 
the  water  between  them,  they  suddenly  fly  apart. 
A  thin  film  of  water  may  be  spread  evenly 
over  a  chemically  clean  glass  plate;  but  if  the 
film  is  touched  with  a  drop  of  alcohol  on  a  thin 

glass  rod,  the  film  will  break,  the  water  retiring  and  leaving  a  dry 

area  around  the  alcohol. 

The  sewing  needle  indents  the  surface  of  the  water  as  if 
the  surface  were  a  tense  membrane  or  skin,  and  tough  enough 
to  support  the  needle.  This  surface  skin  is  weaker  in  alcohol 
than  in  water;  hence  the  bits  of  wood  are  pulled  apart  and 
the  water  is  withdrawn  from  the  spot  weakened  with  alcohol. 

35.  Surface   Tension.  —  The   molecules   composing   the 
surface  of  a  liquid  are  not  under  the  same  conditions  of 
equilibrium  as  those  within  the  liquid.     The  latter  are 

''attracted  equally  in  all  directions 
by  the  surrounding  molecules,  while 
those  at  the  surface  are  attracted 
downward  and  laterally,  but  not  up- 
ward (Fig.  22).  The  result  is  an 
unbalanced  molecular  force  toward 
the  interior  of  the  liquid,  so  that 
the  surface  layer  is  compressed  and 
tends  to  contract.  The  contraction 

means  that  the  surface  acts  like  a  stretched  membrane, 
which  molds  the  liquid  into  a  volume  with  as  small  a 
surface  as  possible.  Liquids  in  small  masses,  therefore, 
always  tend  to  become  spherical. 


FIGURE  22.  —  MOLECULAR 
ATTRACTIONS. 


ILLUSTRATIONS 


31 


FIGURE  23.  —  CIRCLE  IN  LIQUID  FILM. 


36.  Illustrations.  —  Tears, 
dewdrops,  and  drops  of  rain  are 
spherical  because  of  the  tension  in 
the  surface  film.  Surface  tension 
rounds  the  end  of  a  glass  rod  or 
stick  of  sealing  wax  when  softened 
in  a  flame.  It  breaks  up  a  small 
stream  of  molten  lead  into  little 
sections,  and  molds  them  into 
spheres  which  cool  as  they  fall  and 
form  shot.  Small  globules  of  mer- 
cury on  a  clean  glass  plate  are  slightly  flattened  by  their  weight, 
but  the  smaller  the  globules  the  more  nearly  spherical  they  are. 

Of  stout  wire  make  a  ring  three  or  four  inches  in 
diameter  with  a  handle  (Fig.  23) .  Tie  to  it  a  loop 
of  soft  thread  so  that  the  loop  may  hang  near  the 
middle  of  the  ring.  Dip  the  ring  into  a  soap  solu- 
tion containing  glycerine,  and  get  a  plane  film.  The 
thread  will  float  in  it.  Break  the  film  inside  the  loop 
with  a  warm  pointed  wire,  and  the  loop  will  spring 
out  into  a  circle.  The  tension  of  the  film  attached 
to  the  thread  pulls  it  out  equally  in  all  directions. 

Interesting  surfaces  may  be  obtained  by  dipping 
skeleton  frames  made  of  stout  wire  into  a  soap  solu- 
tion.    The  films  in  Fig.  24  are  all   plane,  and  the   angles  where 
three  surfaces  meet  along  a  line  are  necessarily  120°  for  equilibrium. 
A  bit  of  gum  camphor  on  warm  water,  quite  free  from  an  oily  film, 
will  spin  around   in   a 
most    erratic 
The  camphor 


manner. 

dissolves 
unequally  at  different 
points,  and  thus  pro- 
duces unequal  weaken- 
ing of  [the  surface  ten 
sion  in  different  direc- 
tions. 

Make  a  tiny  wooden 
boat  and  cut  a  notch  in 
the  stern  ;  in  this  notch 


FIGURE    24. 
PLANE  FILMS. 


FIGURE  25.  —  BOAT  DRAWN  BY  SURFACE  TENSION. 


32 


MOLECULAR  PHYSICS 


FIGURE  26.  — 
CONTRACTION  OF 
SOAP  BUBBLE. 


put  a  piece  of  camphor  gum  (Fig.  25).  The  cam- 
phor will  weaken  the  tension  astern,  while  the  ten- 
sion at  the  bow  will  draw  the  boat  forward. 

Surface  tension  makes  a  soap  bubble  contract. 
Blow  a  bubble  on  a  small  funnel  and  hold  the  open 
tube  near  a  candle  flame  (Fig.  26).  The  expelled 
air  will  blow  the  flame  aside,  and  the  smaller  the 
bubble  the  more  energetically  will  it  expel  the  air. 

A  small  cylinder  of  fine  wire  gauze  with  solid 
ends,  if  completely  immersed  in  water  and  partly 
filled,  may  be  lifted  out  horizontally  and  still  hold 
the  water.  A  film  fills  the  meshes  of  the  gauze 
and  makes  the  cylinder  air-tight;  if  the  film  is 
broken  by  blowing  sharply  on  it,  the  water  will  quickly  run  out. 

37.  Capillary  Elevation  and  Depression.  —  If  a  fine  glass 
tube,  commonly  called  a  capillary  or  hairlike  tube,  is 
partly  immersed  vertically  in  water,  the  water  will  rise 
higher  in  the  tube  than  the  level  outside ;  on  the  other 
hand,  mercury  is  depressed  below  the  outside  level.  The 
top  of  the  little  column  of  water  is  con- 
cave, while  that  of  the  column  of  mercury 
is  convex  upward  (Fig.  27). 

Familiar  examples  of  capillary  action  are  numer- 
ous. Blotting  paper  absorbs  ink  in  its  fine  pores, 
and  oil  rises  in  a  wick  by  capillary  action.  A 
sponge  absorbs  water  for  the  same  reason ;  so  also 
does  a  lump  of  sugar.  A  cotton  or  a  hemp  rope 
absorbs  water,  increases  in  diameter,  and  shortens. 
A  liquid  may  be  carried  over  the  top  of  a  vessel 
by  capillary  action  in  a  large  loose  cord.  Many 
salt  solution  c  construct  their  own  capillary  high- 
way up  over  the  top  of  the  open  glass  vessel  in  which  they  stand. 
They  first  rise  by  capillary  action  along  the  surface  of  the  glass,  then 
the  water  evaporates,  leaving  the  salt  in  fine  crystals,  through  which 
the  solution  rises  still  higher  by  capillary  action.  This  process  may 
continue  until  the  liquid  flows  over  the  top  and  down  the  outside  of 
the  vessel. 


FIGURE  27.  — 
CONCAVE  AND 
CONVEX  SURFACES 
IN  TUBES. 


CAPILLARY  ACTION  IN   SOILS 


33 


38.  Laws  of  Capillary  Action.  —  Support  vertically  several 
clean  glass  tubes  of  small  internal  diameter  in  a  vessel  of  pure  water 
(Fig.  28).     The  water  will  rise  in  these 

tubes,  highest  in  the  one  of  smallest  di- 
ameter, and  least  in  the  one  of  greatest. 
With  mercury  in  place  of  water,  the  de- 
pression will  be  the  greatest  in  the  smallest 
tube. 

If  two  chemically  clean  glass  plates,  in- 
clined at  a  very  small  angle,  be  supported 
with  their  lower  edges  in  water,  the  height 
to  which  the  water  will  rise  at  different 
points  will  be  inversely  as  the  distance  be- 
tween the  plates,  and  the  water  line  will  FIGURE  28. CAPILLARY 

be  curved  as  in  Fig.  29.  ELEVATIONS. 

These  experiments  illustrate  the  following  laws  : 

I.  Liquids  ascend  in 
tubes  when  they  wet  them, 
that  is,  when  the  surface 
is  concave;  and  they  are 
depressed  when  they  do  not 
wet  them,  that  is,  when  the 
surface  is  convex. 

H-  -^or  tubes  of  small 
diameter,  the  elevation  or  depression  is  inversely  as  the 
diameter  of  the  tube. 

39.  Capillary  Action  in  Soils.  —  The  distribution  of  mois- 
ture in  the  soil  is  greatly  affected  by  capillarity.     Water 
spreads  through  compact  porous  soil  as  tea  spreads  through 
a  lump  of  loaf  sugar.     As  the  moisture  evaporates  at  the 
surface,  more  of  it  rises  by  capillary  action  from  the  sup- 
ply below.     To  conserve  the  moisture  in  dry  weather  and 
in  "  dry  farming,"  the  surface  of  the  soil  is  loosened  by 
cultivation,  so  that  the  interstices  are  too  large  for  free 


» 


FIGURE  29.  —  CAPILLARY     ELEVATION 
BETWEEN  PLATES. 


34 


MOLECULAR  PHYSICS 


FIGURE  30.  — • 
ELEVATION  BY 
SURFACE  TEN- 
SION. 


capillary  action.     The  moisture  then  remains  at  a  lower 
level,  where  it  is  needed  for  the  growth  of  plants. 

40.  Capillarity  Related  to  Surface  Tension.  —The  attrac- 
tion of  water  for  glass  is  greater  than  the  attraction  of 

water  for  itself  (§  12).  When  a  liquid  is 
thus  attracted  by  a  solid,  the  liquid  wets  it 
and  rises  with  a  concave  surface  upward 
(Fig.  30).  The  surface  tension  in  a  curved 
film  makes  the  film  contract  and  produces 
a  pressure  toward  its  center  of  curvature,  as 
shown  in  the  case  of  the  soap  bubble  (§  36). 
When  the  surface  of  the  liquid  in  the  tube 
is  concave,  the  result  of  this  pressure  toward 
the  center  of  curvature  is  a  force  upward  ; 
the  downward  pressure  of  the  liquid  under 
the  film  is  thus  reduced,  and  the  liquid  rises 
until  the  weight  of  the  column  AE  down- 
ward just  equals  the  amount  of  the  upward  force.  When 
the  liquid  is  of  a  sort  like  mercury,  which  does  not  wet 
the  tube,  the  top  of  the  column  is  convex,  the  pressure 
of  the  film  toward  its  center  of  curvature  is  downward,  and 
the  column  sinks  until  the  downward  pressure  is  counter 
balanced  by  the  upward  pressure  of  the  liquid  outside. 

III.   MOLECULAR  FORCES  IN  SOLIDS 

41.  Solution  of  Solids.  —  The  solution  of  certain  solids  in 
liquids  has  become  familiar  by  the  use  of  salt  and  sugar 
in  liquid  foods.     The  solubility  of  solids  is  limited,  for  it 
depends  on  the  nature  of  both  the  solid  and  the  solvent,  — 
the  liquid  in  which  it  dissolves.     At  room  temperatures, 
table  salt  dissolves  about  three  times  as  freely  in  water  as 
in  alcohol ;  while  grease,  which  is  practically  insoluble  in 
water,  dissolves  readily  in  benzine  or  gasoline. 


^^^p 


COMMON  CRYSTALS. 

Quartz  (ideal).  Quartz  (actual). 

Galena  or  Lead  Sulphide.  Garnet. 

Alum. 


CRYSTALLIZATION  35 

Solution  in  a  small  degree  takes  place  in  many  unsuspected  cases. 
Thus,  certain  kinds  of  glass  dissolve  to  an  appreciable  extent  in  hot 
water.  Many  rocks  are  slightly  soluble  in  water,  and  the  familiar 
adage  that  the  "  constant  dropping  of  water  wears  away  a  stone  "  is 
accounted  for,  in  part  at  least,  by  the  solution  of  the  stone.  Flint 
glass,  out  of  which  cut  glass  vessels  are  made,  dissolves  to  some  extent 
in  aqua  ammonia ;  this  liquid  should  not  be  kept  in  cut  glass  bottles, 
nor  should  cut  glass  be  washed  in  water  containing  ammonia. 

There  is  a  definite  limit  to  the  quantity  of  a  solid  which 
will  dissolve  at  any  temperature  in  a  given  volume  of  a 
liquid.  For  example,  360  g.  of  table  salt  will  dissolve  in 
a  liter  of  water  at  ordinary  temperatures;  this  is  equiva- 
lent to  three  quarters  of  a  pound  to  the  quart.  When  the 
solution  will  dissolve  no  more  of  the  solid,  it  is  said  to  be 
saturated.  As  a  general  rule,  though  it  is  not  without 
exceptions,  the  higher  the  temperature,  the  larger  the 
quantity  of  a  solid  dissolved  by  a  liquid.  A  liquid  which 
is  saturated  at  a  higher  temperature  is  supersaturated  when 
cooled  to  a  lower  one. 

42.  Crystallization.  —  When  a  saturated  solution  evapo- 
rates, the  liquid  only  passes  off  as  a  vapor;  the  dissolved 
substance  remains  behind  as  a  solid.  When  the  solid 
thus  separates  slowly  from  the  liquid  and  the  solution 
remains  undisturbed,  the  conditions  are  favorable  for  the 
molecules  to  unite  under  the  influence  of  their  mutual 
attractions,  and  they  assume  regular  geometric  forms 
called  crystals.  Similar  conditions  exist  when  a  saturated 
solution  cools  and  becomes  supersaturated.  The  presence 
of  a  minute  crystal  of  the  solid  then  insures  the  formation 
of  more.  The  process  of  the  separation  of  a  solid  in  the 
form  of  crystals  is  known  as  crystallization. 

Dissolve  100  gm.  of  common  alum  in  a  liter  of  hot  water.  Hang 
some  strings  in  the  solution  and  set  aside  in  a  quiet  place  for  several 
hours.  The  strings  will  be  covered  with  beautiful  transparent  octa- 


36  MOLECULAR  PHYSICS 

hedral crystals.  Copper  sulphate  may  be  used  in  place  of  the  alum; 
large  blue  crystals  will  then  collect  on  the  strings. 

Filter  a  saturated  solution  of  common  salt  and  set  aside  for  twen- 
ty-four hours.  An  examination  of  the  surface  will  reveal  groups  of 
crystals  floating  about.  Each  one  of  these,  when  viewed  through  a 
magnifying  glass,  will  be  found  to  be  a  little  cube. 

Ice  is  a  compact  mass  of  crystals,  and  snow  consists  of  crystals 
formed  from  the  vapor  of  water.  They  are  of  various  forms  but  all 
hexagonal  in  outline  (Fig.  31  ).1 


FIGURE  31.  —  SNOW  CRYSTALS. 

43.  Elasticity.  —  Apply  pressure  to  a  tennis  ball,  stretch 
a  rubber  band,  bend  a  piece  of  watch  spring,  twist  a  strip 
of  whalebone.  In  each  case  the  form  or  the  volume  has 
been  changed,  and  the  body  has  been  strained.  A  strain 
means  either  a  change  in  size  or  a  change  in  shape.  As 
soon  as  the  distorting  force,  or  stress,  has  been  withdrawn, 
these  bodies  recover  their  initial  shape  and  dimensions. 
The  word  stress  is  applied  to  the  forces  acting,  while  the 
word  strain  is  applied  to  the  effect  produced.  The  property 
of  recovery  from  a  strain  when  the  stress  is  removed  is  called 
elasticity.  It  is  called  elasticity  of  form  when  a  body  re- 
covers its  form  after  distortion  ;  and  elasticity  of  volume 
when  the  temporary  distortion  is  one  of  volume.  Gases 
and  liquids  have  perfect  elasticity  of  volume,  because 


1  These  figures  were  made  from  microphotographs  taken  by  Mr.  W.  A. 
Bentley,  Jericho,  Vermont. 


HOOKERS  LAW  37 

they  recover  their  former  volume  when  the  original  pres- 
sure is  restored.  They  have  no  elasticity  of  form.  Some 
solids,  such  as  shoemaker's  wax,  lead,  putty,  and  dough, 
when  long-continued  force  is  applied,  yield  slowly  and 
never  recover. 

The  elasticity  of  a  body  may  be  called  forth  by  pressure, 
by  stretching,  by  bending,  or  by  twisting.  The  bound- 
ing ball  and  the  popgun  are  illustrations  of  the  first  ; 
rubber  bands  are  familiar  examples  of  the  second  ;  bows 
and  springs  of  the  third  ;  and  the  stretched  spiral  spring 
exemplifies  the  fourth. 

44.  Hooke's  Law.  — Solids  have  a  limit  to  their  distor- 
tion, called  the  elastic  limit,  beyond  which  they  yield  and 
are  incapable  of  re- 
covering their  form 
or  volume.  The 
elastic  limit  of  steel 
is  very  high  <,  steel 
breaks  before  there 

is  much  permanent    FlGURE  32. -BENDING  PROPORTIONAL  TO  WEIGHT. 

distortion.    On  the 

other  hand,   lead  does  not  recover  completely  from  any 

distortion. 

When  the  strain  in  an  elastic  body  does  not  exceed  the 
elastic  limit,  in  general  the  distortion  is  proportional  to  the 
distorting  force,  or  the  strain  is  proportional  to  the  stress, 
This  relation  is  known  as  Hookes  law. 

Clamp  a  meter  stick  to  a  suitable  support  (Fig.  32),  and  load  the 
free  end  with  some  convenient'  weight  in  a  light  scale  pan  ;  observe 
the  bending  of  the  stick  by  means  of  the  vertical  scale  and  the  pointer. 
Then  double  the  weight  and  note  the  new  deflection.  It  should  be 
double  the  first.  The  amount  of  bending  or  distortion  of  the  bar  is 
proportional  to  the  weight. 


38  MOLECULAR  PHYSICS 

Generally,  for  all  elastic  displacements  within  the 
elastic  limit,  the  distortions  of  any  kind,  due  to  bending, 
stretching,  or  twisting,  are  proportional  to  the  forces  pro- 
ducing them. 

Questions  and  Exercises 

1.  When  a  glass  tube  or  rod  is  cut  off  its  edges  are  sharp.     Why 
do  they  become  rounded  by  softening  in  a  blowpipe  flame  ? 

2.  Why  does  a  small  vertical  stream  of  water  break  into  drops? 

3.  Why  does  a  dish  with  a  sharp  lip  pour  better  than  one  with- 
out it? 

4.  A  soap  bubble  is  filled  with  air.     Is  the  air  inside  denser  or 
rarer  than  the  air  outside  ? 

5.  Explain  the  action  of  gasoline  in  removing  grease  spots.     How 
should  it  be  applied  so  as  to  avoid  the  dark  ring  which  often  remains 
after  its  use  ? 

6.  The  hairs  of  a  camel's-hair  brush  separate  when  placed  in  water, 
but  gather  to  a  point  when  the  brush  is  removed  from  the  water. 
Explain. 

7.  Are  the    divisions  on  the    scale  of   a  spring  balance  equal  ? 
What  law  is  illustrated  ? 

8.  In  the  stone  quarries  of  ancient  Egypt  it  is  said  that  large 
blocks  of  stone  were  loosened  by  drilling  a  series  of  holes  in  the  rock, 
driving  in  wooden  plugs,  and  then  thoroughly  wetting  them.     Ex- 
plain. 

9.  Why  is  it  difficult  to  write  on  clean  glass  with  a  pen? 

10.  Analysis  of  the  air  in  a  closed  room  shows  little  or  no  difference 
in  its  composition  in  different  parts  of  the  room.     Explain. 

11.  If  a  capillary  tube  is  supported  vertically  in  a  vessel  of  water 
and  the  tube  is  shorter  than  the  distance  to  which  water  would  rise 
in  it,  will  the  water  flow  out  of  the  top  ?     Why  ? 

12.  If  water  rises  15  mm.  in  a  capillary  tube  of  1.9  mm.  diameter, 
what  must  be  the  diameter  of  a  tube  in  which  water  will  rise  45  mm.  ? 


CHAPTER   III 
MECHANICS  OF  FLUIDS 
I.    PRESSURE   OF  FLUIDS 

45.  Characteristics  of  Fluids.  —  A  fluid  has  no  shape  of 
its  own,  but  takes  the  shape  of  the  containing  vessel.     It 
cannot  resist  a  stress  unless  it  is  supported  on  all  sides. 
The  molecules  of  a  fluid  at  rest  are  displaced  by  the  slight- 
est force;  that  is,  a  fluid  yields  to  the  continued  applica- 
tion of  a  force  tending  to  change  its  shape.     -But  fluids 
exhibit  wide  differences  in  mobility,  or  readiness  in  yield- 
ing to  a  stress.      Alcohol,  gasoline,  and  sulphuric  ether 
are  examples  of  very  mobile  liquids;    glycerine  is  very 
much  less  mobile,  and  tar  still  less  so. 

In  fact,  liquids  shade  off  gradually  into  solids.  A  stick 
of  sealing  wax  supported  at  its  ends  yields  continuously 
to  its  own  weight;  in  warm  weather  paraffin  candles  do 
not  maintain  an  upright  position  in  a  candlestick,  but 
curve  over  or  bend  double;  a  cake  of  shoemaker's  wax 
on  water,  with  bullets  on  it  and  corks  under  it,  yields  to 
both  and  is  traversed  by  them  in  opposite  directions.  At 
the  same  time,  sealing  wax  and  shoemaker's  wax  when 
cold  break  readily  under  the  blow  of  a  hammer. 

46.  Viscosity.  —  The  resistance  of  a  fluid  to  flowing  under 
stress  is  called  viscosity.     It  is  due  to  molecular  friction. 
The  slowness  with  which  a  tine  precipitate,  thrown  down 
by  chemical  action,  settles  in  water  is  owing  to  the  vis- 
cosity of  the  liquid;   and  the  slow  descent  of  a  cloud  is 

39 


40 


MECHANICS   OF  FLUIDS 


accounted  for  by  the  viscosity  of  the  air.  Viscosity  varies 
between  wide  limits.  It  is  less  in  gases  than  in  liquids; 
hot  water  is  less  viscous  than  cold  water;  hence  the  rela- 
tive ease  with  which  a  hot  solution  filters. 


THE  MOBILITY  OF  GASOLINE  VAPOR. 

In  this  six-cylinder  automobile  engine,  gasoline  from  the  tank  at  the 
right  is  vaporized  in  the  carburetor  at  the  center.  The  mobility  of  the 
vapor  is  so  great  that  it  passes  readily  through  the  pipe  to  the  cylinders. 

47.  Liquids  and  Gases.  —  Fluids  are  divided  into  liquids 
and  gases.  Liquids,  such  as  water  and  mercury,  are  but 
slightly  compressible,  while  gases,  such  as  air  and  hydro- 
gen, are  highly  compressible.  A  liquid  offers  great  resist- 
ance to  forces  tending  to  diminish  its  volume,  while  a  gas 
offers  relatively  small  resistance.  Water  is  reduced  only 


PASCAL'S  PRINCIPLE 


41 


0.00005  of  its  volume  by  a  pressure  equal  to  that  of  the 

atmosphere  (practically  15  Ib.  to  the  square  inch),  while 

air  is  reduced  to  one  half  its  volume  by  the  same  additional 

pressure.     Pressure  means  force  per  unit  of 

surface.     Then,  too,  gases  are  distinguished 

from  liquids  by  the  fact  that  any  mass  of  gas 

when  introduced  into  a  closed  vessel  always 

completely  fills  it,  whatever  its  volume.     A 

liquid  has  a  bulk  of  its  own,  but  a  gas  has 

not,  since  a  gas  expands  indefinitely  as  the 

pressure  on  it  decreases. 

48.  Pressure  Transmitted  by  a  Fluid.  —  Fit  a 

perforated  stopper  to  an  ounce  bottle,  preferably  with 
flat  sides,  and  mounted  in  a  suitable  frame  (Fig.  33). 
Fill  the  bottle  with  water  and  then  force  a  metal 
plunger  through  the  hole  in  the  stopper.  If  the  plunger  fits  the 
stopper  water-tight,  the  force  applied  to  the 
plunger  will  be  transmitted  to  the  water  as  a 
bursting  force ;  and  the  whole  force  transmitted 
to  the  inner  surface  of  the  bottle  will  be  as  many 
times  greater  than  the  force  applied  as  the  area 
of  this  surface  is  greater  than  that  of  the  end  of 
the  plunger. 

Figure  34  is  a  form  of  syringe  made  of  glass ; 
the  hollow  sphere  at  the  end  has  several  small 
openings.  Fill  with  water  and  apply  force  to 
the  piston.  The  water  will  escape  in  a  series  of 
jets  of  apparently  equal  velocities,  although  only 
one  of  them  is  directly  in  line  with  the  piston. 

Fit  a  glass  tube  to  the  stem  of  a  small  rubber 
balloon;  blow  into  the  tube;  the  balloon  will  ex- 
pand equally  in  all  directions,  forming  a  sphere 
and  showing  equal  pressures  in  all  directions. 
A  large  soap  bubble  shows  the  same  thing. 

49.  Pascal's  Principle.  —  A  solid  transmits  pressure  only 
in  the  direction  in  which  the  force  acts ;  but  a  fluid  trans- 


A77 

r  RESSURE       IN       /\LU 

DIRECTIONS. 


42 


MECHANICS   OF  FLUIDS 


mits  pressure  in  every  direction.     Hence  the  law  first 
announced  by  Pascal  in  1653  : 

Pressure  applied  to  an  inclosed  fluid  is  transmitted 
equally  in  all  directions  and  without  diminution  to 
every  part  of  the  fluid  and  of  the  interior  of  the  contain- 
ing vessel. 

This  is  the  fundamental  law  of  the  mechanics  of  fluids. 
It  is  a  direct  consequence  of  their  mobility,  and  it  applies 
to  both  liquids  and  gases. 

50.  The  Hydraulic  Press.  —  An  important  application  of 
Pascal's  principle  is  the  hydraulic  press.  Figure  35  is  a 

section  showing  the  principal 
parts.  A  heavy  piston  P  works 
water-tight  in  the  larger  cylin- 
der A,  while  in  the  smaller  one 
the  piston  p  is  moved  up  and 
down  as  a  force  pump;  it  pumps 
water  or  oil  from  the  reservoir  D 
and  forces  it  through  the  tube  0 
into  the  cylinder  A.  When  the 
piston  p  of  the  pump  is  forced 
down,  the  liquid  transmits  the 
pressure  to  the  base  of  the  larger 
piston,  on  which  the  force  R  is  as  many  times  the  force  E 
applied  to  p  as  the  area  of  the  large  piston  is  greater  than 
the  area  of  the  small  one.  If  the  cross-sectional  area  of 
the  small  piston  is  represented  by  a,  and  that  of  the  large 
one  by  A,  the  ratio  between  the  forces  acting  on  the  two 
pistons  is  S= JL-O2 

E     a      cP' 


FIGURE  35.  —  HYDRAULIC 
PRESS. 


where  D  and  d  are  the  diameters  of  the  large  and  small 
pistons  respectively. 


Galileo  Galilei  (1566- 
1642)  was  born  at  Pisa,  Italy. 
He  was  a  man  of  great  gen- 
ius, and  an  experimental 
philosopher  of  the  first  rank. 
He  was  educated  as  a  phys- 
ician, but  devoted  his  life  to 
mathematics  and  physics. 
He  discovered  the  properties 
of  the  pendulum,  invented 
the  telescope  bearing  his 
name,  and  was  ardent  in  his 
support  of  the  doctrine  that 
the  earth  revolves  around 
the  sun.  Besides  his  original 
work  in  physics,  he  made  interesting  discoveries  in  astronomy* 


Blaise  Pascal  (1623-1662) 
was  born  at  Clermont  in  Au- 
vergne.  He  was  both  a  math- 
ematician and  a  physicist. 
Even  as  a  youth  he  showed 
remarkable  learning,  and  at 
the  age  of  seventeen  achieved 
renown  with  a  treatise  on 
conic  sections.  He  is  best 
known  for  his  announcement 
in  1653  of  the  important  law 
of  fluid  pressure  bearing  his 
name.  He  distinguished  him- 
self by  his  researches  in  conic 
sections,  in  the  properties  of 
the  cycloid,  and  the  pressure  of  the  atmosphere 


APPLICATION  OF  THE  HYDRAULIC  PRESS 


48 


Thus,  if  the  area  A  is  100  times  the  area  a,  a  force  of 
10  pounds  on  the  piston  p  becomes  1000  pounds  on  P. 
The  hydraulic  press  is  a  device  which  permits  of  the  exer- 
tion of  enormous  forces. 

51.  Application  of  the  Hydraulic  Press. —  This  machine  is 
used  in  the  industries  for  lifting  very  heavy  weights  and 
for  compressing  materials  into  small  volumes.  Instances 
of  the  former  use  are  the  lifting  of  large  crucibles  filled 


FIGURE  i3o.  —  COMMERCIAL  HYDRAULIC  PRESS. 

with  molten  steel,  and  of  locomotives  to  replace  them  on 
the  track.  The  enormous  force  of  the  hydraulic  press  is 
applied  also  to  the  baling  of  cotton  and  paper,  to  punching 
holes  through  steel  plates,  to  making  dies,  embossing  metal, 
and  forcing  lead  through  a  die  in  the  manufacture  of  lead 
pipe.  A  small  white  pine  board  one  inch  thick,  compressed 
in  an  hydraulic  press  to  a  thickness  of  three-eighths  inch, 
becomes  capable  of  a  high  polish  and  has  many  of  the 
properties  of  hard  wood. 

The  commercial  press  (Fig.  36)  is  the  same  in  principle 
as  Fig.  35,  with  the  addition  of  some  auxiliary  parts  to 


44 


MECHANICS   OF  FLUIDS 


make  a  working  machine.  The  piston  s  of  the  force  pump 
may  be  worked  by  any  convenient  power.  It  has  a  check 
valve  d  which  closes  when  «  rises  and  prevents  the  return 
of  the  water  from  the  large  working  cylinder.  The  piston 
P  is  surrounded  by  a  peculiar  leather  collar,  without  which 
the  press  is  a  failure.  The  larger  the  pressure  in  P,  the 
closer  the  leather  collar  presses  against 
the  piston  and  prevents  leakage.  The 
upper  portion  of  the  machine,  cut  away 
in  the  figure,  differs  according  to  the  use 
to  which  the  press  is  put. 

If  the  ratio  between  the  cross-sections 
of  the  two  pistons  is  500,  then  when  8  is 
pressed  down  with  a  force  of  100  Ib.  the 
piston  P  is  forced  up  with  a  force  of 
50,000  Ib. 

In  the  hydraulic  press  it  is  evident  that 
the  small  piston  travels  as  many  times 
farther  than  the  large  one  as  the  force 
exerted  by  the  large  piston  is  greater 
than  the  effort  applied  to  the  small  one. 
52.  The  Hydraulic  Elevator.  —  A  mod- 
ern application  of  Pascal's  principle  is 
the  hydraulic  elevator.  A  simple  form 
is  shown  in  Fig.  37.  A  long  piston  P 
carries  the  cage  A,  which  runs  up  and 
down  between  guides  and  is  partly  coun- 
terbalanced by  a  weight  W.  The  piston 
runs  in  a  tube  0  sunk  in  a  pit  to  a  depth 
equal  to  the  height  to  which  the  cage  is 
designed  to  rise.  Water  under  pressure  enters  the  pit 
from  the  pipe  m  through  the  valve  v.  Turned  in  one 


FIGURE  37.  —  HY- 
DRAULIC    ELEVATOR. 


direction  the  valve  admits^  water  to  the  sunken  cylinder, 


DOWNWARD   PRESSUEE  OF  A   LIQUID 


45 


and  the  pressure  forces  the  piston  up  ;  when  the  operator 
turns  it  in  the  other  direction  by  pulling  a  cord,  it  allows 
the  water  to  escape  into  the  sewer,  and  the  elevator  de- 
scends by  its  own  weight. 

When  greater  speed  is  required,  the  cage  is  connected 
to  the  piston  indirectly  by  a  system  of  pulleys.  The  cage 
then  usually  runs  four  times  as  fast  and  four  times  as  far 
as  the  piston. 

53.  Downward  Pressure  of  a  Liquid.  —  Pascal's  principle 
relates  to  the  transmission  of  pressure  applied  to  a  liquid 
in  a  closed  vessel.  But  a  liquid  in  an  open  vessel,  such 
as  water  in  a  bucket,  produces  pressure  because  it  is 
heavy  ;  and  the  pressure  of  any  layer  is  transmitted  to 
every  other  layer  at  a  lower 
level.  Since  each  layer  adds  t 
its  pressure,  there  must  be  in- 
creasing pressure  as  the  depth  ' 
increases. 


A  glass  cylinder,  5,  is  cemented  into 
a  metal  ferule,  T,  which  screws  into 
a  short  cylinder,  D  (Fig.  38).  This 
short  cylinder  is  closed  at  the  bottom 
by  an  elastic  diaphragm  of  thin  metal, 
any  motion  of  which  caused  by  water 
in  B  is  communicated  by  a  rack  and 
pinion  device  to  the  hand  on  the  dial,  FIGURE  38.  —  DOWNWARD  PRES- 
E.  As  the  tank,  A,  filled  with  water  SURE  PROPORTIONAL  TO  DEPTH 
is  moved  up  the  supporting  rod  water  flows  through  the  tube,  F, 
into  the  cylinder,  B,  causing  the  hand  to  move  over  the  dial.  The 
reading  of  the  hand  divided  by  the  depth  of  the  water  in  B  at  any 
moment  will  be  practically  constant.  Hence, 

The  downward  pressure  is  proportional  to  the  depth. 

Repeat  the  experiment  with  a  saturated  solution  of  common  salt, 
which  is  heavier  than  water.     Every  pointer  reading  will  be  greater 


46 


MECHANICS  OF  FLUIDS 


than  the  corresponding  ones  with  water,  but  the  same  relation  will 
exist  between  them.     Hence, 

The  downward  pressure  of  a  liquid 
is  proportional  to  its  density  (§  69). 

54.  Upward  Pressure.  —  Let  a  glass 
cylinder  A  (Fig.  39),  such  as  a  straight  lamp 
chimney,  have  its  bottom  edge  ground  off  so 
as  to  be  closed  water  tight  by  a  thin  piece  of 
glass  0.  Holding  this  against  the  bottom  of 
the  cylinder  by  means  of  a  thread  C,  immerse 
the  cylinder  in  water.  The  thread  may  then 
be  released  and  the  bottom  will  stay  on  be- 
cause the  water 
presses  up  against 
it.  To  release  the 
bottom  we  shall 


FIGURE  39.  —  UPWARD 
PRESSURE. 


have  to  pour  water  into  the  cylinder  until  the 
levels  inside  and  outside  are  the  same,  The 
upward  pressure  on  the  bottom  of  the  cylinder 
is  then  the  same  as  the  downward  pressure 
inside  at  the  same  depth.  Or, 

In  liquids  the  pressure  upward  is 
equal  to  the  pressure  downward  at 
any  depth. 

55.  Pressure  at  a  Point  — The  three 
glass  tubes  of  Fig.  40  have  short  arms  of  the 
same  length,  measured  from  the  bend  to  the 
mouth.  They  open  in  different  directions, 
—  upward,  downward,  and  sidewise.  Place 
mercury  to  the  same  depth  in  all  the  tubes, 
and  lower  them  into  a  tall  jar  filled  with 
water.  When  the  open  ends  of  the  short 
arms  are  kept  at  the  same  level,  the  change 
in  the  level  of  the  mercury  is  the  same  in  all 
of  them.  Hence, 

The  pressure  at  a  point  in  a  liquid  is  the  same  in  all 
directions. 


FIGURE  40. — PRESSURE 
SAME  IN  ALL  DIRECTIONS. 


TOTAL  FORCE  ON  ANY  SURFACE  47 

The  equality  of  pressure  in  all  directions  may  also  be 
inferred  from  the  absence  of  currents  in  a  vessel  of  liquid, 
since  an  unbalanced  pressure  would  produce  motion  of 
the  liquid. 

56.  Bottom    Pressure    Inde- 
pendent of    the   Shape  of  the 
Vessel.  —  Proceeding  as   in  §  53, 
use  in  succession  the  three  vessels 
shown  in  Fig.  41.     They  have  equal 
bases,  but  differ  in  shape  and  vol- 
ume.    Thev  are  known  as  Pascal's    —  _,  T 

J  FIGURE  41.  —  PRESSURE    INDEPEND- 

vases.    Fill  each  in  succession  to  ENT  OF  SHAPE. 

the  same  height,  and  note  the  read- 
ing of  the  pointer.     It  will  be  the  same  for  all,  notwithstanding  the 
great  difference  in  .the  amount  of  water.     Hence, 

The  downward  pressure  in  a  liquid  is  independent  of 
the  shape  of  the  vessel. 

The  apparent  contradiction  of  unequal  masses  of  a 
liquid  producing  equal  pressures  is  known  as  the  hydro- 
static paradox. 

Thus,  suppose  the  circular  bottom  of  a  tin  pail  has  an  area  of 
200  cm.2  It  would  be  about  16  cm.  in  diameter.  Suppose  the  pail 
filled  with  water  to  a  depth  of  25  cm.  Then  the  pressure  on  the 
bottom  would  be  the  weight  of  a  prism  of  water  1  cm.2  in  section 
and  25  cm.  high,  or  25  g.,  since  a  cm.8  of  water  weighs  one  gram. 

The  whole  force  on  the  bottom  would  be  200  x  25  =  5000  g.,  or 
5  kg.  If  the  pail  flares,  it  would  contain  more  than  5000  cm.8  of 
water  and  would  require  more  than  5  kg.  of  force  to  lift  it,  but  the 
pressure  on  the  bottom  would  be  the  same. 

57.  Total  Force  on  Any  Surface.  —  It  will  be  seen  from 
the  example  in  the  last  section  that  the  pressure  on  any 
area  is  equal  to  the  product  of  its  depth  h  below  the  sur- 
face of  the  liquid  and  the  weight  d  of  a  unit  volume  of 
the  liquid,  or  p  =  lid.     If  the  depth  is  in  centimeters  and 


48  MECHANICS  OF  FLUIDS 

the  weight  in  grams,  the  pressure  p  in  water  is  equal  to 
the  depth  A,  since  a  cubic  centimeter  of  water  weighs  one 
gram.  The  pressure  is  then  in  grams  per  square  centi- 
meter. But  if  h  is  in  feet  and  d  in  pounds  per  cubic  foot, 
then  jt?  =  Ax62.4  pounds  per  square  foot,  since  a  cubic 
foot  of  water  weighs  62.4  pounds.  To  get  the  pressure 
in  pounds  per  square  inch,  divide  by  144,  because  there 
are  144  square  inches  in  a  square  foot. 

The  force  on  any  horizontal  area  A  is  then 

P  —  A  x  h  x  d     .     .     (Equation  1) 

If  the  given  surface  is  inclined,  then  the  pressure  in- 
creases from  its  value  at  the  highest  point  submerged  to 
its  value  at  the  lowest  point.  In  this  case  h  means  the 
mean  depth  of  the  area,  or  the  depth  of  its  center  of  figure. 
The  total  force  on  any  given  plane  area  is  always  normal, 
that  is,  perpendicular  to  it.  Equation  1  still  applies, 

Examples.  To  calculate  the  force  on  the  bottom  and  sides  of  a 
cubical  box  30  centimeters  on  each  edge,  filled  with  water,  and  stand- 
ing on  a  horizontal  plane  : 

The  area  of  each  face  is  30  x  30  =  900  cm.2  Then  the  force  on 
the  bottom  at  a  depth  of  30  cm.  is  900  x  30  =  27,000  g.  On  the  sides 

the  pressure  varies  from  zero  to 
30  g.  per  square  centimeter.  The 
average  pressure  is  halfway  down 
at  a  point  15  cm.  deep  and  is  15 
g.  per  square  centimeter.  Hence 

the  force  tending  to  push  out  each 
FIGURE  42.  — FORCE  AGAINST  DAM.        .      .  &      *  Knr. 

side  is  900  x  15  =  13,500  g. 

The  upstream  face  of  a  dam  measures  20  ft.  from  top  to  bottom, 
but  it  slopes  so  that  its  center  of  figure  is  only  7  ft.  from  the  surface 
of  the  "water  when  the  dam  is  full  (Fig.  42).  Find  the  perpendicular 
force  against  the  dam  for  every  foot  of  length. 

The  area  of  the  face  of  the  dam  per  foot  in  length  is  20  sq.  ft. 
Hence  the  weight  of  the  column  of  water  to  represent  the  force  is 
20  x  7  x  62,4  =  8736  Ib. 


LEVEL   OF  LIQUID  IN  CONNECTED    VESSELS        49 


FIGURE  43.  —  SAME   LEVEL   IN 
ALL  BRANCHES. 


58.  Surface  of  a  Liquid  at  Rest.  —  The  free  surface  of  a 
liquid  under  the  influence  of  gravity  alone  is  horizontal. 
Even  viscous  liquids  assume  a  hori- 
zontal surface  in  course  of  time. 

The  sea,  or  any  other  large  ex- 
panse of  water,  is  a  part  of  the 
spheroidal  surface  of  the  earth. 
When  one  looks  with  a  field  glass 
at  a  long  straight  stretch  of  the 
Suez  Canal  near  Port  Said,  the 
water  and  the  retaining  wall  as 
contrasting  bodies  appear  dis- 
tinctly curved  as  a  portion  of  the 
rounded  surface  of  the  earth. 

59.  Level  of  Liquid  in  Connected 

Vessels.  —  The  water  in  the  apparatus  of  Fig.  43  rises  to 

the  same  level  in  all  the 
branches.  (Why  should  the 
spout  of  a  teakettle  be  as  high 
as  the  lid  ?)  There  is  equi- 
librium because  the  pressures 
on  opposite  sides  of  any  cross 
section  of  the  liquid  in  the 
connecting  tube  are  equal, 
since  they  are  due  to  liquid 
columns  of  the  same  height. 

The  glass  water  gauge,  used  to 
show  the  height  of  the  water  in  a 
steam  boiler,  is  an  important  appli- 
cation of  this  principle.     A  thick- 
FIGURE  44.  -  WATER  GAUGE.         wal]ed  glagg  ^  ^  (pig>  ^  .g 

connected  at  the  top  with  the  steam  and  at  the  bottom  with  the  water 
in  the  boiler.  The  pressure  of  steam  is  then  the  same  on  the  water  in 
the  boiler  and  in  the  gauge  tube,  and  the  water  level  is  the  same  in 


50  MECHANICS  OF  FLUIDS 

the  two.  The  stopcocks  C  and  D  are  kept  open  except  when  it  be« 
comes  necessary  to  replace  the  glass  tube.  Another  stopcock  E  serves 
to  clean  out  the  tube  by  running  steam  through  it. 

Another  application  is  the  water  level,  consisting  of  two  glass  tubes, 
joined  by  a  long  rubber  tube,  and  employed  by  builders  for  leveling 
foundations. 

60.  Artesian  Wells. — Artesian  or  flowing  wells  illustrate  on  a 
grand  scale  the  tendency  of  water  to  "  seek  its  level."  In  geology  an 
artesian  basin  is  one  composed  of  long  strata  one  above  the  other. 
One  of  these  permits  the  passage  of  water,  and  lies  .between  two  layers 
of  clay  or  other  material  through  which  water  does  not  pass  (Fig.  45). 


FIGURE  45.  —  ARTESIAN  WELL. 

This  stratum  K  crops  out  at  some  higher  level  and  here  the  water 
finds  entrance.  When  a  well  I  is  bored  through  the  overlying  strata 
in  the  valley,  water  issues  on  account  of  the  pressure  transmitted  from 
higher  points  at  a  distance.  There  are  8000  or  10,000  artesian  wells 
in  the  western  part  of  the  United  States ;  some  notable  ones  are  at 
Chicago,  St.  Louis,  New  Orleans,  Charleston,  and  Denver.  In  Europe 
there  are  very  deep  flowing  wells  in  Paris  (2360  ft.),  Berlin  (4194  ft.), 
and  near  Leipzig  (5740  ft.). 

61.  City  Water  Supply.  —  In  some  cases,  where  a  supply 
of  water  for  city  purposes  is  available  at  an  elevation 
higher  than  the  points  of  distribution,  as  in  San  Francisco, 
Los  Angeles,  Denver,  and  New  York,  the  water  from  the 
source,  or  from  a  storage  reservoir,  is  conducted  to  the  city 
in  open  channels,  or  in  pipes  or  "  mains,"  and  the  pressure 
causing  it  to  flow  is  due  to  gravity  alone.  Arriving  at  the 


ELEPHANT  BUTTE  DAM. 

Largest  mass  of  masonry  in  the  world.  The  lake  formed  by  the  dam  is 
45  miles  long  and  has  a  capacity  four  times  that  of  the  Assouan  Dam 
in  Rcrvnt  f.nmicrh  tn  rnver  the  state  of  Delaware  to  B.  death  of  two  feet. 


CITY  WATER  SUPPLY 


51 


city,  it  is  distributed  through  the  streets,  the  pipes  ter- 
minating at  fire  hydrants  in  the  streets,  and  at  plugs  and 
faucets  in  buildings.  The  water  is  under  pressure  ade- 
quate to  carry  it  to  the  highest  desired  points. 

In  the  absence  of  a  water  supply  at  an  elevation,  it  is 
necessary  to  pump  the  water  into  a  reservoir  on  a  high 


FIGURE  46.  —  CITY  WATER  SUPPLY. 

point,  or  into  a  "  staridpipe"  or  water  tower  as  a  part  of  the 
distributing  system.  The  water  rises  in  the  water  tower 
to  a  height  corresponding  to  the  pressure  maintained  by 
the  pump.  This  device  serves  to  equalize  the  pressure 
throughout  the  system,  and 
in  the  smaller  systems  it 
may  take  the  place  of  a 
reservoir ;  it  may  exert 
pressure  for  domestic  pur- 
poses and  for  fire  protec- 
tion even  when  the  pump 
is  not  running  (Fig.  46). 

For  limited  domestic  supply  the  hydraulic  ram  (Fig.  47)  is  some- 
times used.  Its  action  depends  on  the  inertia  of  a  stream  of  water 
in  a  pipe.  The  valve  at  B  is  normally  open  and  the  other  valve  open- 
ing upward  into  the  air  dome  is  closed.  The  flow  of  water  through 
the  pipe  A  closes  the  ball  valve  B,  and  the  shock  of  the  sudden  arrest 
of  the  flow  opens  the  valve  into  the  air  dome ;  the  water  enters  to  re- 
lieve the  sudden  pressure.  Valve  B  then  opens  again  and  the  other 
one  closes.  The  flow  thus  takes  place  by  a  succession  of  pulses. 


FIGURE  47.  —  HYDRAULIC  RAM. 


52  MECHANICS   OF  FLUIDS 

Questions  and  Problems 

1.  If  a  pressure  gauge  be  attached  to  the  water  pipe  on  the  top 
floor  of  a  tall  building  and  a  second  one  be  attached  in  the  basement, 
will  the  readings  be  the  same  ?    Why  ? 

2.  Why  is  there  danger  of  bursting  a  thermos  bottle  by  forcing 
in  the  stopper  when  the  bottle  is  full  of  liquid  ? 

3.  In  a  city  supplied  with  water  from  a  reservoir,  to  what  height 
will  the  water  rise  in  a  vertical  pipe  connected  with  the  system  ? 

4.  Why  does  a  coiled  garden  hose  tend  to  straighten  out  when 
the  water  is  turned  on  ? 

5.  Is  the  pressure  against  a  dam  that  backs  up  the  water  for  a 
mile  greater  than  on  one  that  backs  up  the  water  for  a  half  mile, 
the  depth  of  water  at  the  dam  being  the  same  in  both  cases  ? 

6.  The  cylinders  of  a  hydraulic  press  are  respectively  6  in.  and 
1  in.  in  diameter.     If  a  force  of  100  Ib.  is  applied  to  the  piston  of  the 
smaller  cylinder,  what  force  will  the  larger  piston  exert  ? 

7.  A  tank  10  ft.  square  and  10  ft.  deep,  full  of  water,  will  -exert 
how  much  force  on  the  bottom  ?    How  much  on  one  side  ? 

8.  A  glass  tube  76  cm.  long  is  full  of  mercury.     What  is  the 
pressure  in  grams  per  cm.2  on  the  bottom  ?    (1  cm.3  of  mercury  weighs 
13.6  g.) 

9.  A  glass  cylinder  6  in.  in  diameter  and  12  in.  deep  is  full  of 
water.     What  is  the  force  of  the  water  against  its  cylindrical  surface  ? 

10.  If  the  pressure  gauge  of  a  water  system  registers  50  Ib.,  how 
high  will  water  rise  in  a  vertical  pipe  attached  thereto  ? 

11.  What  weight  can  be  supported  on  the  platform  of  a  hydraulic 
elevator,  if  the  piston  is  10  in.  in  diameter  and  the  pressure  gauge 
register  50  Ib.  to  the  square  inch  ? 

12.  Sea  water  weighs  64  Ib.  to  the  cubic  foot.     What  force  will  be 
exerted  on  a  board  10  ft.  long  and  1  ft.  wide  sunk  horizontally  in  the 
sea  to  a  depth  of  a  mile  ? 

13.  The  pressure  gauge  of  a  water  system  registers  60  Ib.  to  the 
sq.  in.  on  the  ground  floor  and  30  Ib.  to  the  sq.  in.  on  the  top  floor. 
What  is  the  difference  of  level? 

14.  A  kerosene  tank  is  10  ft.  in  diameter  and  10  ft.  deep.     When 


THE  MEASURE  OF  BUOYANCY  53 

full  of  kerosene  what  force  will  there  be  against  the  cylindrical  sur- 
face ?     (One  cubic  foot  of  kerosene  weighs  54  Ib.) 

15.  A  wooden  box  one  foot  square  has  fitted  into  its  top  a  vertical 
tube  40  ft.  long  and  1  in.  in  diameter.  When  both  the  tube  and  box 
are  full  of  water  what  bursting  force  is  exerted  on  the  inner  surface 
of  the  box? 

II.   BODIES   IMMERSED  IN  LIQUIDS 

62.  Buoyancy.  —  A  marble  sinks  in  water  and  floats  in 
mercury ;  a  fresh  egg  sinks  in  water  and  floats  in  a  satu- 
rated solution  of  common  salt;   a  piece  of  oak  floats  in 
water  and  the  dense  wood  lignum-vitae  sinks ;  a  swim- 
mer in  the  sea .  is  nearly  lifted  off  his  feet  by  the  heavy 
salt  water. 

Suspend  a  pound  or  two  of  iron  from  the  hook  of  a  draw  scale, 
and  note  its  weight.  Now  bring  a  beaker  of  water  up  under  the  iron 
and  partly  immerse  it ;  note  that  its  weight  is  diminished;  immerse 
farther  and  the  loss  of  weight  increases ;  after  it  is  fully  submerged, 
the  loss  of  weight  does  not  increase  with  the  depth  of  immersion. 
If  salt  water  is  used,  the  apparent  loss  of  weight  will  be  greater ;  if 
kerosene,  it  will  be  less.  In  popular  language  the  body  immersed  is 
said  to  have  lost  weight.  Its  real  weight  has  not  changed  in  the 
least;  bat  an  upward  force  has  been  brought  to  bear  on  it. 

The  lifting  force  of  a  liquid  on  a  body  immersed  in  it 
is  called  buoyancy. 

63.  The  Measure  of  Buoyancy.  —  The   law  of   buoyancy 
was  discovered  by  a  Greek  philosopher  Archimedes  about 
240  B.C.  while  engaged  in   determining  the  composition 
of  the  golden  crown  of  Hiero,  king  of  Syracuse,  who  sus- 
pected that  the  goldsmith  had  mixed  silver  with  the  gold. 
The  law  is  as  follows  : 

JL  body  immersed  in  a  liquid  is  buoyed  up  by  a  force 
equal  to  the  weight  of  the  liquid  displaced  by  it. 


54 


MECHANICS  OF  FLUIDS 


The  following  experiments  illustrate  the  principle  of  Archimedes, 
which  is  the  basis  of  the  theory  of  floating  bodies : 

The  hollow  brass  cylinder  A  (Fig.  48)  and  the 
solid  brass  cylinder  B,  which  exactly  fits  into  A,  are 
suspended  from  one  arm  of  a  balance  and  carefully 
counterpoised.  If  now  the  cylinder  A  be  filled  with 
water,  the  equilibrium  will  be  disturbed ;  but  if  at 
the  same  time  cylinder  B  is  immersed  in  water,  as  in 
the  figure,  the  equilibrium  will  be  restored.  The 
upward  force  on  the  solid  cylinder  is  therefore  equal 
to  the  weight  of  the  water  in  A,  and  this  is  equal 
in  volume  to  that  of  the  immersed  cylinder.  If  the 
experiment  is  tried  with  any  other  liquid  which 
does  not  attack  brass,  the  result  will  be  the  same. 

A  metal  cylinder  5.1  cm.  long,  and  2.5  cm.  in  di- 
ameter has   a  volume  of    almost   exactly  25  cm.8 
Suspend  it  by  a  fine  thread  from  one  arm  of  a  balance 
(Fig.  49)  and  counterpoise.     Then  submerge  it  in 
water  as  in  the  figure.     The  equilibrium  will  be  re- 
stored by  placing  25  g.  in  the  pan  above  the  cylinder. 
The  cylinder  displaces  25  cm.8  of 
water  weighing  25  g.,  and  its  ap- 
parent loss  of  weight  is  25  g.  The  temperature  of 
the  water  should  be  near  freezing. 

64.  Explanation  of  Archimedes'  Principle. 

—  If  a  cube  be  immersed  in  water  (Fig. 
50),  the  pressures  on  the  vertical  sides  a 
and  b  are  equal  and  in  opposite  direc- 
tions. The  same  is  true  of  the  other 
pair  of  vertical  faces.  There  is  therefore 
no  resultant  horizontal  force.  On  d  there 
is  a  downward  force  equal  to  the  weight 
of  the  column  of  water  having  the  face  d 
as  a  base,  and  the  height  dn.  On  c  there 
is  an  upward  force  equal  to  the  weight  of  a  column  of 
water  whose  base  is  the  area  of  c,  and  whose  height  is  en. 


FIGURE  48.  — 
ILLUSTRATING 
PRINCIPLE  OF 
ARCHIMEDES. 


FIGURE  49.  —  Ai - 
PARENT  LOSS  OF 
WEIGHT. 


FLOATING  BODIES  55 

The  upward  force  therefore  exceeds  the  downward  force 
by  the  weight  of  the  prism  of  water  whose  base  is  the  face 
c  of  the  cube,  and  whose  height  is  the  difference  between 
en  and  dn,  or  cd.     This  is  the 
weight  of  the  liquid  displaced 
by  the  cube. 

In  general  if  a  cube  of  any 
material  be  immersed  in  water, 
the  water  pressure  at  every  point 
will  be  independent  of  the  sub- 
stance of  the  cube.  Suppose 
then  it  is  a  cube  of  the  water 

itself.      Its    weight    will     be    a     Fioure  50.  -  EXPLANATION    OF 

PRINCIPLE. 
vertical  force  downward.     But 

it  is  in  equilibrium,  for  it  does  not  move.  Hence  its 
own  weight  downward  is  offset  by  an  equal  force  acting 
vertically  upward.  But  this  upward  force  of  the  water 
is  the  same,  whatever  the  material  of  the  cube.  Hence, 
there  is  an  upward  force  on  any  submerged  cube  equal 
to  the  weight  of  the  water  displaced  by  it.  A  similar 
argument  applies  to  a  body  of  any  shape  submerged  in 
any  liquid. 

65.  Floating  Bodies.  —  If  a  body  be  immersed  in  a 
liquid,  it  may  displace  a  weight  of  the  liquid  less  than, 
equal  to,  or  greater  than  its  own  weight.  In  the  first 
case,  the  upward  force  is  less  than  the  weight  of  the  body, 
and  the  body  sinks.  In  the  second  case,  the  upward 
force  is  equal  to  the  weight  of  the  body,  and  the  body  is 
in  equilibrium.  In  the  third  case,  the  upward  force  ex- 
ceeds the  weight  of  the  body,  and  the  body  rises  until 
enough  of  it  is  out  of  the  liquid  so  that  these  forces  be- 
come equal.  The  buoyancy  is  independent  of  the  depth 
so  long  as  the  body  is  wholly  immersed,  but  it  decreases 


56 


MECHANICS  OF  FLUIDS 


as  soon   as  the  body  begins  to  emerge   from  the  liquid. 
Hence, 

When  a  body  floats  on  a  liquid  it  sinks  to  such  a  depth 
that  the  weight  of  the  liquid  displaced  equals  its  own 
weight. 

66.  Experimental  Proof.  —  Make  a  wooden  bar  20  cm.  long  and 
1  cm,  square  (Fig.  51).  Drill  a  hole  in  one  end  and  fill  with  enough 
shot  to  give  the  bar  a  vertical  position  when  float- 
ing with  nearly  its  whole  length  in  water.  Gradu- 
ate the  bar  in  millimeters  along  one  edge^  beginning 
at  the  weighted  end,  and  coat  with  hot  paraffin. 
Weigh  the  bar  and  float  it  in  water,  noting  the  vol- 
ume in  cubic  centimeters  immersed.  This  volume 
is  equal  to  the  volume  of  water  displaced;  and 
since  1  cm.3  of  water  weighs  1  g.,  the  weight  of  the 
water  displaced  is  numerically  equal  to  the  volume 
of  the  bar  immersed.  This  will  be  found  also  very 
nearly,  if  not  quite,  equal  to  the  weight  of  the 
loaded  bar. 

67.  The  Cartesian  Diver.  —  Descartes,  a 
French  scientist,  illustrated  the  principle  of  flota- 
tion by  means  of  an  hydrostatic 
toy,  since  called  the  Cartesian 
diver.  It  is  made  of  glass,  is 
hollow,  and  has  a  small  opening 
near  the  bottom.  The  figure  is 
partly  filled  with  water  so  that 
it  just  floats  in  a  jar  of  water  (Fig.  52).  Pressure 
applied  to  the  sheet  rubber  tied  over  the  top  of  the 
jar  is  transmitted  to  the  water,  more  water  enters 
the  floating  figure,  and  the  air  is  compressed. 
The  figure  then  displaces  less  water  and  sinks. 
When  the  pressure  is  relieved,  the  air  in  the  diver 
expands  and  forces  water  out  again.  The  actual 
displacement  of  water  is  then  increased,  and  the 
figure  rises  to  the  surface.  The  water  in  the  diver 
may  be  so  nicely  adjusted  that  the  little  figure  will  sink  in  cold 
water,  but  will  rise  again  when  the  water  has  reached  the  tempera- 
ture of  the  room,  and  the  air  in  the  figure  has  expanded. 


FIGURE  51.  — 
EXPERI MENTAL 
PROOF. 


FIGURE  52. —  CAR- 
TESIAN DIVER. 


THE  FLOATING   DRY  DOCK 


57 


FIGURE  53. — A  UNITED  STATES  SUBMARINE. 

A  good  substitute  for  the  diver  is  a  small  inverted  homeopathic  vial 
in  a  flat  16-oz.  prescription  bottle,  filled  with  water  and  closed  with  a 
rubber  stopper.  When  pressed,  the  sides  yield,  and  the  vial  sinks. 

A  submarine  boat  is  a  modern  Cartesian  diver  on  a  large  scale.  It 
is  provided  with  tight  compartments,  into  which  water  may  be  ad- 
mitted to  make  it  sink.  It  may  be  made  to  rise  to  the  surface  by  ex- 
pelling some  of  the  water  by  powerful  pumps. 

68.  The  Floating  Dry  Dock.  —  The  floating  dock  re- 
sembles the  submarine  in  principle.  It  is  made  buoyant 


THE  SAME  SUBMARINE  SUBMERGING. 


58 


MECHANICS  OF  FLUIDS 


FIGURE  54.  —  DRY  DOCK. 


by  pumping  water  out  of  water-tight 
compartments,  and  by  floating  it  lifts 
a  vessel  out  of  the  water.  In  Fig.  54 
J.,  A  are  compartments  full  of  air. 
When  they  are  filled  with  water, 
the  dock  sinks  to  the  dotted  position 
j5,  B  and  the  vessel  is  floated  into  it. 
When  the  water  is  pumped  out, 
the  dock  takes  the  position  indi- 
cated by  the  full  lines  and  the  vessel 
is  lifted  out  of  water. 


III.  DENSITY  AND  SPECIFIC  GRAVITY 

69.  Density.  —  We  are  familiar  with  the  fact  that  bodies 
of  different  kinds  may  have  the  same  size  or  bulk  and  yet 
differ  greatly  in  weight,  that  is,  in  mass.  A  block  of  steel, 
for  example,  is  nearly  forty  times  as  heavy  as  a  block  of 
cork  of  the  same  dimensions,  that  is,  its  mass  is  nearly 
forty  times  as  great.  This  difference  is  expressed  as  a 
difference  in  density.  The  density  of  a  substance  is  the 
number  of  units  of  mass  of  it  contained  in  a  unit  of  volume. 

In  the  e.g. s.  system  density  is  the  number  of  grams  per 
cubic  centimeter.  For  example,  the  density  of  steel  is  7.816 
grams  per  cubic  centimeter  (expressed  as  7.816  g. /cm.3), 
while  that  of  cork  has  a  mean  value  of  about  0.2  g./cm.3, 
and  that  of  mercury  13.596  g./cm.3  So 


mass 


or  in  symbols, 


j  •  ,  //e-M/ort 

density  = , 

volume 


m 


d  =  — ;  whence  m  =  dv,  and  v  =  — 
v  d 


(Equation  2) 


To  illustrate,  a  slab  of  marble  20  x  50  x  2  cm.  has  a  volume  of 
2000  cm.8  and  weighs  5.4  kg.  or  5400  g.  Hence  its  density  is  5400/2000 
=  2.7  g./cm.8 


DENSITY  AND  SPECIFIC  GRAVITY  COMPARED     59 

70.  Specific  Gravity.  —  The  specific  gravity  of  a  body  is 
the  ratio  of  its  weight  to  the  weight  of  an  equal  volume  of 
water.     If,  for  example,  a  cubic  inch  of  lead  weighs  11.36 
times  as  much  as  a  cubic  inch  of  water,  the  specific  gravity 
of  lead  is  11.36.     The  principle  of  Archimedes  furnishes 
a  simple  method  of  finding  specific  gravity,  since  the  loss 
of  weight  of  a  heavy  body  suspended  in  water  is  equal  to 
the  weight  of  the  water  displaced,  or  the  weight  of  a  vol- 
ume of  water  equal  to  that  of  the  suspended  body.     Hence 

./.  .,  weight  of  body 

specific  gravity  = *     .-'     ,    y        • 

loss  of  weight  in  water 

For  example,  a  piece  of  copper  weighs  880  g.  in  air  and  780  in 
water.  Its  loss  of  weight  is  then  100  g.,  and  this  is  the  weight  of  the 
water  displaced.  Hence  the  specific  gravity  of  copper  is  880/100  =  8.8. 

71.  Density   and    Specific    Gravity   Compared.  —  Specific 
gravity  and  density  have  not  quite  the  same  meaning.     For 
example,  the  specific  gravity  of  lead  is  the  abstract  num- 
ber 11.36,  while  the  density  of  lead  is  11.36  g. /cm.3,  or 
62.4x11.36  =  708.9   Ib./cu.    ft.,   both   of   them    concrete 
numbers. 

Specific  gravity  is  only  a  ratio  between  two  masses  or 
weights,  and  is  therefore  independent  of  the  units  em- 
ployed in  determining  it ;  while  density  depends  on  the 
units  used  to  express  it. 

In  the  e.g.  s.  system  density  and  specific  gravity  are 
numerically  the  same,  because  the  density  of  water  is  one 
gram  per  cubic  centimeter,  or 

density  (g./cm.3)  =  specific  gravity. 

But  in  the  English  system 

density  (Ib./cu.  ft.)  =  62.4  x  specific  gravity. 


60 


MECHANICS   OF  FLUIDS 


It  is  worth  remembering  that  if  the  density  of  any  sub- 
stance is  expressed  in  c.  g.  8.  units,  its  numerical  value  is 
always  that  of  the  specific  gravity.  Table  IV  in  the 
Appendix  of  this  book  gives  the  densities  in  grams  per 
cubic  centimeter. 

72.  Density  of  Solids.  —  The  density  of  a  solid  body  is 
its  mass  divided  by  its  volume.  Its  mass  may  always  be 
obtained  by  weighing,  but  the  volume  of  an  irregular  solid 
cannot  be  obtained  from  a  measurement  of  its  dimensions. 
In  the  c.  g.  8.  system,  however,  the  principle  of  Archimedes 
furnishes  a  simple  method  of  finding  the  volume  of  a  solid, 
however  irregular  it  may  be ;  for  in  this  system  the  volume 
of  an  immersed  solid  is  numerically  equal  to  its  loss  of 
weight  in  water  (§  63).  Then  the  equa- 
tion which  defines  density  (§  69), 


mass 


becomes 
density 


volume 
mass  of  body 


loss  of  weight  in  water 


FIGURE  55.  — 
SOLIDS  HEAVIER 
THAN  WATER.  ' 


73.  Solids  Heavier  than  Water.  —  Find 
the  mass  of  the  body  in  air  in  terms  of 
grams;  if  it  is  insoluble  in  water,  find 
its  apparent  loss  of  weight  by  suspending 
it  in  water  (Fig.  55).  This  loss  of 
weight  is  equal  to  the  weight  of  the  volume  of  water  dis- 
placed by  the  solid  (§  63).  But  the  volume  of  a  body  in 
cubic  centimeters  is  the  same  as  the  mass  in  grams  of  an 
equal  volume  of  water.  The  mass  divided  by  this  volume 
is  the  density. 

74.    Solids  Lighter  than  Water.  —  If  the  body  floats,  its 
volume  may  still  be  obtained  by  tying  to  it  a  sinker  heavy 


SOLIDS  LIGHTER   THAN    WATER 


61 


enough  to  force  it  beneath  the  surface.  Let  wl  denote  the 
weight  in  grams  required  to  counterbalance  when  the  body 
is  in  the  air,  and  the  attached  sinker  in  the  water ;  and 
let  w2  denote  the  weight  to  counterbalance  when  both  body 
and  sinker  are  under  water  (Fig.  56). 
Then  obviously  w1  —  w2  is  equal  to  the 
upward  force  on  the  body  alone,  and  is 
therefore  numerically  equal  to  the  volume 
of  the  body.  The  mass  divided  by  this 
volume  is  the  density. 

If  the  solid  is  soluble  in  water,  a  liquid  of 
known  density,  in  which  the  body  is  not 
soluble,  must  be  used  in  place  of  water. 
Then  the  loss  of  weight  is  equal  to  the 
weight  of  the  liquid  displaced,  and  if  this        FIGURE    56.  — 
is   divided  by   the    density   of  the  liquid    SoLIDS     LlGHTER 
(Equation   2),   the   volume   of  the  body 
will  be  obtained.     Then  the  mass  of  the  body  divided  by 
this  volume  will  be  the  density  sought. 

EXAMPLES.  —  First,  for  a  body  heavier  than  water. 

Weight  of  body  in  air  •    .t, .  •    ••    ;     •     •     •     10.5  g. 

Weight  of  body  in  water 6.3  g. 

Weight  of  water  displaced 4.2  g. 

Since  the  density  of  water  is  1  g.  per  cubic  centimeter,  the  volume 
of  the  water  displaced  is  4.2  cm.8.  This  is  also  the  volume  of  the 
body.  Therefore,  10.5  -H  4.2  =  2.5  g.  per  cubic  centimeter  is  the 
density. 

Second,  for  a  body  lighter  than  water. 

Weight  of  body  in  air 4.8  g. 

Weight  of  sinker  in  water 10.2  g. 

Weight  of  body  and  sinker  in  water  ...       8.4  g. 

The  combined  weight  of  the  body  in  air  and  the  sinker  in  water 
is,  then,  4.8  +  10.2  =  15  g.  But  when  the  body  is  attached  to  the 


62 


MECHANICS  OF  FLUIDS 


sinker,  their  apparent  combined  weight  is  only  8.4  g.  Therefore 
the  buoyant  effort  on  the  body  is  15  —  8.4  =  6.6  g.,  and  this  is  the 
weight  of  the  water  displaced  by  the  body,  and  hence  its  volume  is 
6.6  cm.8.  The  density  is,  then,  4.8  -4-  6.6  =  0.73  g.  per  cubic  centimeter. 
Third,  for  a  body  soluble  in  water.  Suppose  it  is  insoluble  in  alcohol, 
the  density  of  which  is  0.8  g.  per  cubic  centimeter. 

Weight  of  body  in  air 4.8  g. 

Weight  of  body  in  alcohol 3.2  g. 

Weight  of  alcohol  displaced 1.6  g. 

The  volume  of  alcohol  displaced  is  1.6  -s-  0.8  =  2  cm.8.  This  is 
also  the  volume  of  the  body.  Therefore,  the  density  of  the  body  is 
4.8  -4-  2  =  2.4  g.  per  cubic  centimeter. 

75.  Density  of  Liquids.  —  (a)  By  the  specific  gravity  bottle. 
A  specific  gravity  bottle  (Fig.  57)  is  usually  made  to  hold 
a  definite  mass  of  distilled  water  at  a 
specified  temperature,  for  example,  25, 
50,  or  100  g.  Its  volume  is  therefore  25, 
50,  or  100  cm.3.  To  use  the  bottle, 
weigh  it  empty,  and  filled  with  the  liquid, 
the  density  of  which  is  to  be  determined. 
The  weight  of  the  liquid  divided  by  the 
capacity  of  the  bottle  in  cubic  centimeters 
(the  number  of  grams)  is  equal  to  the 
density  of  the  liquid. 

(b)  By  the  density  bulb. 
The  density  bulb  is  a  small 
glass  globe  loaded  with  shot, 
and  having  a  hook  for  suspension  (Fig.  58).  To 
use  it,  suspend  from  the  arm  of  a  balance  with 
a  fine  platinum  wire,  and  weigh  first  in  air  and 
then  in  water.  The  apparent  loss  of  weight  is 
the  weight  of  the  water  displaced  by  the  bulb. 
Then  weigh  it  again  when  suspended  in  the  liquid.  The 
loss  of  weight  is  this  time  the  weight  of  a  volume  of  the 


FIGURE  57.  — 
SPECIFIC  GRAVITY 
BOTTLE. 


FIGURE  58. 
—  DENSITY 
BULB. 


DENSITY  OF  LIQUIDS 


63 


liquid  equal  to  that  of  the  bulb.     Divide  this  loss  of  weight 

by  the  loss  in  water,  and  the  quotient  will  be  the  specific 

gravity  of   the   liquid,  or   its   density   in 

grams  per  cubic  centimeter  (§  71). 

(e)    By  the  hydrometer.     The  common 

hydrometer  is  usually  made  of  glass,  and 

consists  of  a  cylindrical  stem  and  a  bulb 

weighted  with  mercury  or  shot  to  make  it 

sink  to  the  required  level  (Fig.  59).     The 

stem  is  graduated,  or  has  a  scale  inside, 

so  that  readings  can  be  taken  at  the  surface 

of  the   liquid   in   which   the  hydrometer 

floats.  These  readings  give  the  densities 
directly,  or  they  may  be  reduced 
to  densities  by  means  of  an  ac- 
companying table.  Hydrom- 
eters sometimes  have  a  ther- 
mometer in  the  stem  to  indicate 
the  temperature  of  the  liquid 
at  the  time  of  taking  the  read- 
ing. Specially  graduated  in- 
struments of  this  class  are  used  to  test  milk, 
alcohol,  acids,  etc. 

For  liquids  lighter  than  water,  in  which  the 
hydrometer  sinks  to  a  greater  depth,  it  is  cus- 
tomary to  use  a  separate  instrument  to  avoid 
so  long  a  stem  and  scale. 
FIGURE  60        -^or  testing  the  acid  of  a  storage  battery,  the 

—  ACID  HY-  hydrometer  is  inclosed  in  a  large  glass  tube  (Fig. 

DROMETER.       60^     By  means  of  ^e  rubber  bulb  at  the  top 

of  the  large  tube  enough  acid  may  be  drawn  in  to  make  the 
hydrometer  float.  The  hydrometer  is  then  read  as  usual 
and  the  acid  is  returned  to  the  cell  by  squeezing  the  bulb. 


FIGURE  59.  —  HY- 
DROMETER. 


64  MECHANICS  OF  FLUIDS 

Questions  and  Problems 

1.  Why  does  an  ocean  steamer  draw  more  water  after  entering 
fresh  water  ? 

2.  If  the  Cartesian  diver  should  sink  in  the  jar,  why  will  the 
addition  of  salt  cause  it  to  rise  ? 

3.  What  is  the  density  of  a  body  weighing  15  g.  in  air  and  10  g 
in  water  ?     What  is  its  specific  gravity  ? 

4.  A  hollow  brass  ball  weighs  1  kg.     What  must  be  its  volume 
so  that  it  will  just  float  in  water? 

5.  What  is  the  density  of  a  body  weighing  20  g.  in  air  and  16  g. 
in  alcohol  whose  density  is  0.8  g.  per  cubic  centimeter? 

6.  A  bottle  filled  with  water  weighed  60  g.  and  when  empty  20  g. 
When  filled  with  olive  oil  it  weighed  56.6  g.     What  is  the  density  of 
olive  oil  ? 

7.  A  density  bulb  weighed  75  g.  in  air,  45  g.  in  water,  and  21  g. 
in  sulphuric  acid.     Calculate  the  density  of  the  sulphuric  acid. 

8.  A  piece   of  wood  weighs  96  g.  in  air,  172  g.  in  water  with 
sinker  attached.     The  sinker  alone  in  water  weighs  220  g.     Find  the 
density  of  the  wood. 

9.  A  piece  of  zinc  weighs  70  g.  in  air,  and  60  g.  in  water.     What 
will  it  weigh  in  alcohol  of  density  0.8  g.  per  cubic  centimeter  ? 

10.  The  mark  to  which  a  certain  hydrometer  weighing  90  g.  sinks 
in  alcohol  is  noted.     To  make  it  sink  to  the  same  mark  in  water  it 
must  be  weighted  with  22.5  g.     What  is  the  density  of  the  alcohol  ? 

11.  A  body  floats  half  submerged  in  water.     What  is  its  specific 
gravity?     What  part  of   it  will  be  submerged   in   alcohol,   specific 
gravity  0.8? 

12.  If  an  iron  ball  weighs  100.4  Ib.  in  air,  what  will  it  weigh  in 
water  if  its  specific  gravity  is  7.8? 

13.  What  is  the  specific  gravity  of  a  wooden  ball  that  floats  two 
thirds  under  water  ? 

14.  A  ferry  boat  weighs  700  tons.     What  will  be  the  displacement 
of  water  if  it  takes  on  board  a  train  weighing  600  tons? 

15.  A  liter  flask  weighing  75  g.  is  half  filled  with  water  and  half 
with  glycerine.     The  flask  and  liquids  weigh  1205  g.     What  is  the 
density  of  the  glycerine?     What  is  its  specific  gravity? 


PRESSURE  PRODUCED  BY    THE  AIR  65 

• 

IV.    PRESSURE  OF  THE  ATMOSPHERE 

76.  Weight  of  Air.  —  It  is  only  a  little  more  than  250 
years  since  it  became  definitely  known  that  air  has  any 
weight  at  all.    Even  now  we  scarcely  appreciate  its  weight. 

Place  a  globe  holding  about  a  liter  (Fig.  61)  on  the  pan  of  a  bal- 
ance and  counterpoise;  the  stopcock  should  be  open.  Remove  the 
globe  and  force  in  more  air  with  a  bicycle  pump,  clos- 
ing the  stopcock  to  retain  the  air  under  the  increased 
pressure;  the  balance  will  show  that  the  globe  is 
heavier  than  before.  Remove  it  again  and  exhaust 
the  air  with  an  air  pump ;  the  balance  will  now  show 
that  the  globe  has  lost  weight.  A  large  incandescent 
lamp  bulb  may  be  used  in  place  of  the  globe  by  first 
counterbalancing  and  then  admitting  air  by  punctur- 
ing with  the  very  pointed  flame  of  a  blowpipe.  Thus 
air,  though  invisible,  may  be  put  into  a  vessel  or  re-  FIGURE  61. 

moved  like  any  other  fluid ;  and,  like  any  other  fluid,    GLOBE    FOR 

it  has  weight.  WEIGHING  AIR. 

The  weight  of  a  body  of  air  is  surprisingly  large.  A 
cubic  yard  of  air  at  atmospheric  pressure  weighs  more 
than  2  Ib.  The  air  in  a  hall  50  ft.  long,  30  ft.  wide,  and 
18  ft.  high  weighs  more  than  a  ton.  Precise  measure- 
ments have  shown  that  air  at  the  temperature  of  freezing 
and  under  a  pressure  equal  to  that  of  a  column  of  mer- 
cury 76  cm.  high  weighs  1.293  g.  per  liter,  or  0.001293  g. 
per  cubic  centimeter. 

77.  Pressure  Produced  by  the  Air.  —  Since  the  air  sur- 
rounding the  earth  has  weight,  it  must  exert  pressure  on 
any  surface  equal  to  the  weight  of  a  column  of  air  above 
it,  just  as  in  the  case  of  a  liquid.      Many  experiments 
prove  this  to  be  true.     We  are  not  aware  of  this  pressure 
because  it  is  equalized  in  all  directions,  and  we  are  built 
to   sustain  it,  just  as  deep-sea  fishes   sustain   the  much 
greater  pressure  of  water  above  them. 


66 


MECHANICS  OF  FLUIDS 


Stretch  a  piece  of  sheet  rubber,  and  tie  tightly  over  the  mouth  of 
a  glass  vessel,  as  shown  in  Fig.  62.  If  the  air  is  gradually  exhausted 
from  the  vessel,  the  rubber  will  be  forced 
down  more  and  more  by  the  pressure  of 
the  air  above  it,  and  it  may  break.  The 
depression  will  be  the  same  in  whatever 
direction  the  rubber  membrane  may  be 
turned. 

Fill  a  common  tumbler  full  of  water, 
cover  with  a  sheet  of  paper  so  as  to  ex- 

FIGURE    62.  —  DOWNWARD    clude  the  air>  and  holdinS  the  hand  against 
PRESSURE  OF  THE  AIR.        the  paper,  invert 
the  tumbler  (Fig. 

63).     When  the  hand  is  removed,  the  paper 

is  held  against  the  mouth  of  the  glass  with 

sufficient  force  to  keep  the  water  from  run- 
ning out. 

Cut  about  20  cm.  from  a  piece  of  glass 

tubing  of  3  or  4  mm.  bore.     Dip  it  vertically 

into  a  vessel  of  water,  and  close  the  upper 

end  with  the  finger.     The  tube  may  now  be 

lifted  out,  and  the  water  will  remain  in  it. 
Figure  64  illustrates  a  pi- 
pette ;  it  is  useful  for  convey- 
ing a  small  quantity  of  liquid  from  one  vessel  to  another. 


FIGURE  63.  —  UPWARD 
PRESSURE  OF  THE  AIR. 


78.    The  Rise  of  Liquids  in  Exhausted  Tubes. 

—  Near  the  close  of  Galileo's  life  his  patron, 
the  Duke  of  Tuscany,  dug  a  deep  well  near 
Florence,  and  was  surprised  to  find  that  he 
could  get  no  pump  in  which  water  would 
rise  more  than  about  32  feet  above  the  level 
in  the  well.  He  appealed  to  Galileo  for  an 
explanation  ;  but  Galileo  appears  to  have  been 
equally  surprised,  for  up  to  that  time  every- 
body supposed  that  water  rose  in  tubes  exhausted  by 
suction  because  "nature  abhors  a  vacuum."  Galileo  sug- 


FIGURE  64. — 
PIPETTE. 


HYDRO -AIRPLANES. 

When  in  the  air  these  are  sustained  by  the  air-pressure  against  their 
planes;  when  on  the  water,  by  the  water-pressure  against  their 
pontoons. 


PASCAL'S  EXPERIMENTS 


67 


gested  experiments  to  find  out  to  what  limit  nature  abhors 
a  vacuum,  but  he  was  too  old  and  enfeebled  in  health  to 
perform  them  himself  and  died  before  the  problem  was 
solved  by  others. 

79.  Torricelli's    Experiment.  —  Torricelli,    a   friend   and 
pupil  of  Galileo,  hit  upon  the  idea  of  measuring  the  resist- 
ance nature  offers  to  a  vacuum  by  a  column  of 
mercury  in  a  glass  tube  instead  of  a  column  of 

water  in  the  Duke  of  Tuscany 's  pump.  The 
experiment  was  performed  in  1643  by  Viviani 
under  Torricelli's  direction. 

A  stout  glass  tube  about  a  yard  long,  sealed 
at  one  end  and  filled  with  clean  mercury,  is 
closed  at  the  open  end  with  the  finger,  and  in- 
verted in  a  vessel  of  mercury  in  a  vertical  po- 
sition (Fig.  65).  When  the  finger  is  removed, 
the  column  falls  to  a  height  of  about  30  inches. 
The  space  above  the  mercury  is  known  as  a 
Torricellian  vacuum.  The  column  of  mercury 
in  the  tube  is  counterbalanced  by  the  pressure 
of  the  atmosphere  on  the  mercury  in  the  larger 
vessel  at  the  bottom. 

80.  Pascal's  Experiments.  —  To  Pascal  is  due 
the   credit   of   completing   the  demonstration 

that  the  weight  of  the  column  of  mercury  in  the  Tor- 
ricellian experiment  measures  the  pressure  of  the  atmos- 
phere. He  reasoned  that  if  the  mercury  is  held  up 
simply  by  the  pressure  of  the  air,  the  column  should  be 
shorter  at  higher  altitudes  because  there  is  then  less  air 
above  it.  Put  to  the  test  by  carrying  the  apparatus  to  the 
top  of  the  Tour  St.  Jacques  (Fig.  66),  150  feet  high, 
at  that  time  the  bell  tower  of  a  church  in  Paris,  his  theory 
was  confirmed.  A  statue  of  Pascal  now  stands  at  the 


FIGURE  65. 
—  TORRICEL- 
LI'S TUBE. 


68 


MECHANICS  OF  FLUIDS 


base  of  the  old  tower.  Desiring  to  carry  the  test  still 
further,  he  wrote  to  his  brother-in-law  to  try  the  experi- 
ment on  the  Puy  de  Dome,  a  mountain  nearly  1000  m. 
high,  in  southern  France.  The  result  was  that  the  column 

of  mercury  was  found  to 
be  nearly  8  cm.  shorter 
than  in  Paris. 

Pascal  repeated  the 
experiment  with  red 
wine  instead  of  mercury, 
and  with  glass  tubes 
forty -six  feet  long  ;  and 
he  found  that  the  lighter 
the  fluid,  the  higher  the 
column  sustained  by  the 
pressure  of  the  air. 
Further,  a  balloon,  half 
filled  with  air,  appeared 
fully  inflated  when  car- 
ried up  a  high  mountain, 
and  collapsed  again  grad- 
ually during  the  descent. 

Thus    the     question    of 
FIGURE  66.  —  TOUR  ST.  JACQUES.  ,,        -^    -,  £     m 

the    Duke    of    Tuscany 

was  fully  answered;  liquids  rise  in  exhausted  tubes  be- 
cause of  the  pressure  of  the  atmosphere  on  the  surface  of 
the  liquid  outside. 

81.  Pressure  of  One  Atmosphere.  —  The  height  of  the 
column  of  mercury  supported  by  atmospheric  pressure 
varies  from  hour  to  hour  and  with  the  altitude  above  the 
sea.  Its  height  is  independent  of  the  cross  section  of  the 
tube,  but  to  find  the  pressure,  or  force  per  unit  area,  a 
tube  of  unit  cross  section  must  be  assumed.  Suppose  an 


THE   HAHOMETEH 


69 


internal  cross-sectional  area  of  1  cm.2.  The  standard 
height  chosen  is  76  cm.  of  mercury  at  the  temperature 
of  melting  ice  (0°  C.),  and  at  sea  level  in  lati- 
tude 45°.  The  density  of  mercury  at  this  tem- 
perature is  13.596  grams  per  cubic  centimeter. 
Hence,  standard  atmospheric  pressure,  which  is 
the  weight  of  this  column  of  mercury,  is 

76  x  13.596  =  1033.3  g.  per  square  cen- 
timeter, or  roughly  1  kg.  per  square 
centimeter,  equivalent  to  14.7 
Ib.  per  square  inch. 

The  height  of  a  column  of  water  to  produce 
ti  pressure  of  one  atmosphere  is  76  x  13.596 
=  1033.3  cm.  =  33.9  ft. 

82.  The  Barometer.  —  The  barometer  is  an 
instrument  based  on  Torricelli's  experiment, 
and  is  designed  to  measure  the  varying  pres- 
sure of  the  atmosphere.  In  its  simplest  form 
it  consists  of  a  J-shaped  glass  tube  about  86 
cm.  (34  in.)  long,  and  attached  to  a  support- 
ing board  (Fig.  67).  The  short  arm  has  a 
piuhole  near  the  top  for  the  admission  of  air. 
A  scale  is  fastened  by  the  side  of  the  tube,  and 
the  difference  of  readings  at  the  top  of  the 
mercury  in  the  long  arm  and  the  short  one  gives 
the  height  of  the  mercury  column  sustained  by 
atmospheric  pressure.  This  varies  from  about 
73  to  76.5  cm.  for  places  near  sea  level.  When 
accuracy  is  required,  the  barometer  reading  ] 
must  be  corrected  for  temperature.  A  good  barometer 
must  contain  pure  mercury,  and  the  mercury  must  be 
boiled  in  the  glass  tube  to  expel  air  and  moisture. 


FIGURE  67. 
—  THE    BA- 


70 


MECHANICS   OF  FLUIDS 


83.  The  Aneroid  Barometer.  —  A  more  convenient  barom- 
eter   to    carry   about  is    the    aneroid    barometer,    which 
contains  no  liquid.     It  consists  essentially  of  a  shallow 
cylindrical  box  (Fig.  68),  from  which  the  air  is  partially 
exhausted.     It  has  a  thin   cover  corrugated  in  circular 

ridges  to  give  it  greater 
flexibility.  The  cover 
is  prevented  from  col- 
lapsing under  atmos- 
pheric pressure  by  a 
stiff  spring  attached  to 
the  center  of  the  cover 
(shown  in  the  figure 
under  the  pointer). 
This  flexible  coyer  rises 
and  falls  as  the  pres- 
sure of  the  atmosphere 
varies,  and  its  motion  is 
transmitted  to  the  pointer  by  means  of  delicate  levers  and 
a  chain.  A  scale  graduated  by  comparison  with  a  mer- 
curial barometer  is  fixed  under  the  pointer.  These  instru- 
ments are  so  sensitive  that  they  readily  indicate  the  change 
of  pressure  when  carried  from  one  floor  of  a  building  to 
the  next,  or  even  when  moved  no  farther  than  from  a  table 
to  the  floor. 

84.  Utility  of  the  Barometer.  —  The  barometer  is  a  faithful 
indicator  of  all  changes  in  the  pressure  of  the  atmosphere. 
These  may  be  due  to  fluctuations  in  the  atmosphere  itself, 
or  to  changes  in  the  elevation  of  the  observer. 

The  barometer  is  constantly  used  by  the  Weather 
Bureau  in  forecasting  changes  in  the  weather.  Experi- 
ence has  shown  that  barometric  readings  indicate  weather 
changes  as  follows  : 


FIGURE  68.  —  ANEROID  BAROMETER. 


CYCLONIC  STORMS 


71 


I.  A   rising   barometer  indicates   the   approach   of  fair 
weather. 

II.  A  sudden  fall  of  the  barometer  precedes  a  storm. 

III.  An  unchanging  high  barometer  indicates  settled  fair 
weather. 

The  difference  in  the  altitude  of  two  stations  may  be 
computed  from  barometer  readings  taken  at  the  two  places 
simultaneously.  Various  complex  rules  have  been  pro- 
posed to  express  the  relation  between  the  difference  in 
barometer  readings  and  the  difference  in  altitude ;  a  sim- 
ple rule  for  small  elevations  is  to  allow  0.1  in.  for  every 
90  ft.  of  ascent. 

85.  Cyclonic  Storms.  —  Weather  maps  are  drawn  from 
observations  made  at  many  places  at  the  same  time  and 
telegraphed  to  a  central 
station.  In  this  way  cy- 
clonic storms  are  discov- 
ered and  followed.  At  the 
center  of  the  storm  is  the 
lowest  reading  of  the  ba- 
rometer. Curves  called 
isobars  are  traced  through 
points  of  equal  pressure 
around  this  center  (Fig. 
69) .  The  wind  blows  from 
areas  of  higher  pressure 
toward  those  of  lower,  but 
in  the  northern  hemisphere 
the  inflowing  winds  are  de- 
flected toward  the  right  on  account  of  the  rotation  of  the 
earth.  This  gives  to  the  storm  a  counter-clockwise  rota- 
tion, as  indicated  by  the  arrows  in  a  weather  map.  Cy- 


FIGURE  69.  —  ISOBARS. 


72  MECHANICS   OF  FLUIDS 

clonic  storms  usually  cross  the  northwest  boundary  of  the 
United  States  from  British  Columbia,  travel  in  a  south- 
easterly direction  until  they  cross  the  Rocky  Mountain 
range,  and  then  turn  northeasterly  toward  the  Atlantic 
coast.  Storms  coming  from  the  Gulf  of  Mexico  usually 
travel  along  the  Atlantic  coast  toward  the  northeast. 

Questions  and  Problems 

1.  What  are  the  objections  to  the  use  of  water  as  the  liquid  for 
barometers  ? 

2.  Why  must  the  air  be  completely  removed  from  the  barometer 
tube? 

3.  Why  is  mercury  the  best  liquid  to  use  in  a  barometer  tube  ? 

4.  Point  out  some  of  the  good  points  as  well  as  some  of  the  objec- 
tionable features  of  an  aneroid  barometer. 

5.  Must  a  barometer  be  suspended  out  of  doors  in  order  to  get 
the  air  pressure  ?     Why  ? 

6.  Does  the  diameter  of  the  bore  of  a  barometer  tube  affect  the 
height  to  which  the  mercury  rises  ? 

7.  How  can  you  make  water  run  in  a  regular  stream  from  a 


8.  The  barometer  reading  is  75.2  cm.    Calculate  the  atmospheric 
pressure  per  square  centimeter. 

9.  The  barometer  reading  is  29  in.     Calculate  the  atmospheric 
pressure  per  square  inch. 

10.  Calculate  the  buoyancy  of  the  air  for  a  ball  10  cm.  in  diameter 
if  a  liter  of  air  weighs  1.29  g. 

II-  The  density  of  glycerine  is  1.26  g.  per  cubic  centimeter.  If  a 
barometer  were  constructed  for  glycerine  what  would  be  its  reading 
when  the  mercurial  barometer  reads  73  cm.  ? 

12,  When  the  density  of  the  air  is  0.0013  g.  per  cubic  centi- 
meter, how  much  less  will  200  cm.3  of  cork  weigh  in  air  than  in  a 
vacuum  ? 


COMPRESSIBILITY  OF  AIR 


73 


12.  If  a  barometer  at  the  foot  of  a  tower  reads  29.5 
in.,  while  one  at  the  top  reads  29.2  in.,  what  is  the  height 
of  the  tower  ? 

13.  A  bottle  is  fitted  air-tight  with  a  rubber  stopper 
and  a  tube  as  in  Fig.  70.     If  water  be  sucked  out  by  the 
tube,  what  will  happen  when  the  tube  is  released?    If 

air  is  blown  in  through  the  tube, 
what  will  happen  when  the  tube  is  re- 
leased? 

14.  Figure  71  represents  a  pneu- 
matic inkstand,  nearly  full  of  ink. 
Why  does  the  ink  not  run  out? 


FIGURE  70. 


FIGURE  71. 


V.    COMPRESSION  AND  EXPANSION  OF  GASES 

86.  Compressibility  of  Air.  —  The  inflation  of  a  toy  bal- 
loon, an  air  cushion,  and  a  pneumatic  tire  illustrates  the 
ready  compressibility  of  the  air. 

Push  a  long  test  tube  under  water  with  its  open  end 
down.  The  deeper  the  tube  is  sunk,  the  higher  the  water 
rises  in  it  and  the  smaller  becomes  the  volume  of  the  in- 
closed air ;  also  the  reaction  tending  to  lift  the  tube  in- 
creases. 

The  expansibility  of  air,  or  its  tendency  to  increase  in 
volume  whenever  the  pressure  is  reduced,  is  shown  by  its 
escape  from  any  vessel  under  pressure,  such  as  the  rush  of 
compressed  air  from  a  popgun,  an  air  gun,  or  a  punctured 
pneumatic  tire.  The  air  in  a  building  shows  the  same 
tendency  to  expand.  When  the  pressure  outside  is  sud- 
denly reduced,  as  in  the  passage  of  a  wave  due  to  an  ex- 
plosion, the  force  of  expansion  of  the  air  within  often 
bursts  the  windows  outward. 

Blow  air  into  the  bottle  (Fig.  70)  through  the  open  tube.  The  air 
forced  in  bubbles  up  through  the  water  and  is  compressed  within. 
As  soon  as  the  tube  is  released  and  the  pressure  in  it  falls  to  that  of 


74 


MECHANICS   OF  FLUIDS 


Air 
Cushion 


the  atmosphere,  the  expansive  force  of  the  imprisoned  air  forces  water 
out  through  the  tube  with  great  velocity.     This  principle  is  applied  in 

many  forms  of  devices  for  spraying 
plants  and  shrubbery. 

The  compression  and  the  expansion 
of  air  are  both  illustrated  by  the  com- 
mon pneumatic  door  check  for  light 
doors ;  also  by  the  air  dome  on  a  force 
pump ;  and  the  air  cushion  on  a  water 
pipe  (Fig.  72),  which  is 
usually  carried  a  few 
inches  higher  than  the 
faucet  so  that  the  air 
confined  in  the  closed 


FIGURE  72.  —  AIR   CUSHION 
WATER  PIPE. 


ON 


-100 


-80 


-60 


end  may  act  as  a  cushion  to  take  up  any  sudden  shock 
due  to  the  inertia  of  the  water  when  the  stream  is  sud- 
denly checked.  The  "  pounding  "  of  the  pipes  when 
the  water  is  turned  off  quickly  is  owing  to  the  absence 
of  this  air  cushion. 

87.  Boyle's  Law.  —  In  dealing  with  air  in  a 
state  of  compression  or  expansion,  the  question 
at  once  arises,  —  how  does  a  given  volume  of 
air  change  when  the  pressure  on  the  air 
changes?  The  answer  is  contained  in  the  dis- 
covery by  Robert  Boyle  at  Oxford,  England, 
in  1662.  The  principle  discovered  by  Boyle 
(and  later  in  France  by  Mariotte)  is  known 
as  Boyle's  law ;  it  applies  to  all  gases  at  a  con- 
stant temperature. 

Boyle  in  his  experiments  used  a  J-tube  with 
the  short  arm  closed ;  both  arms  were  pro- 
vided with  a  scale  (Fig.  73).  In  his  experi- 
ments the  pressures  extended  only  from  -fa  of 
an  atmosphere  to  4  atmospheres. 

Mercury  was  poured  in  until  it  stood  at  the  same  level  in  both  arms 
of  the  tube.     The  air  in  the  short  arm  was  then  under  the  same  pres- 


-110 


-no 


o 


FIGURE  73. 
—  BOYLE'S 
EXPERIMENT. 


THE  LAW  APPROXIMATE  75 

sure  as  the  atmosphere  outside.  Its  volume  was  noted  by  means  ot 
the  attached  scale,  and  more  mercury  was  then  poured  into  the  tube, 
The  difference  in  the  level  of  the  mercury  in  the  two  arms  of  the  tube 
gave  the  excess  of  pressure  on  the  inclosed  air  above  that  of  the  at- 
mosphere. When  this  difference  amounted  to  76  cm.,  the  pressure  on 
the  gas  in  the  short  tube  was  2  atmospheres,  and  its  volume  was  re- 
duced to  one  half.  When  the  difference  became  twice  76  cm.,  the 
pressure  on  the  inclosed  air  was  3  atmospheres  and  its  volume  became 
one  third ;  and  so  on. 

This  is  the  law  of  the  compressibility  of  gases ;  it  may 
be  expressed  as  follows : 

At  a  constant  temperature  the  volume  of  a  given  mass 
of  gas  varies  inversely  as  tJw  pressure  sustained  by  it. 

If  the  volume  of  gas  v  under  a  pressure  p  becomes 
volume  v'  when  the  pressure  is  changed  to  p1 ',  then  by  the 
law:  , 

^-  =  •2^-;  whence  pv  =p'vf.       (Equation  3) 

(Notice  the  inverse  proportion.)  In  other  words,  the 
product  of  the  volume  of  the  gas  and  the  corresponding 
pressure  remains  constant  for  the  same  temperature. 

88.  The  Law  Approximate.  —  Extended  investigations 
have  shown  that  Boyle's  law  is  not  rigorously  exact  for 
any  gas.  In  general,  gases  are  more  compressible  than 
the  law  requires,  and  this  is  especially  true  for  gases  which 
are  easily  liquefied,  such  as  carbon  dioxide  (CO2),  sulphur 
dioxide  (SO2),  and  chlorine.  Within  moderate  limits  of 
pressure,  however,  Boyle's  law  is  exceedingly  useful  in 
dealing  with  the  volume  and  pressure  of  gases. 

An  example  will  illustrate  its  use :  If  a  mass  of  gas  under  a  pres- 
sure of  72  cm.8  of  mercury  has  a  volume  of  1900  cm.8,  what  would  its 
volume  be  if  the  pressure  were  76  cm.8?  By  Equation  3,  pv  =  p'v' ] 
hence,  72  x  1900  =  76  x  v'.  From  this  equation  v'  =  1800  cm.8. 


76 


MECHANICS   OF  FLUIDS 


FIGURE  74.  —  SECTION  OF 
AIR  COMPRESSOR. 


89.  The  Air  Compressor.  —  A  pump  designed  to  compress 
air  or  other  gases  under  a  pressure  of  several  atmospheres 
is  shown  in  section  in  Fig.  74,  and 
complete  in  Fig.  75.  The  piston  is 
solid,  and  there  are  two  metal  valves 
at  the  bottom.  Air  or  other  gas  is 
admitted  through  the  left-hand  tube 
when  the  piston  rises ;  when  it  de- 
scends, it  compresses 
the  inclosed  air,  the 
pressure  closes  the 
left-hand  valve,  and 

opens  the  outlet  valve  on  the  right,  and 
the  compressed  air  is  discharged  into  the 
compression  tank. 

A  bicycle  pump  (Fig.  76)  is  an 
air  compressor  of  a  very  simple 
type.  The  piston  has  a  cup- 
shaped  leather  collar  e,  which 
permits  the  air  to  pass  by  into 
the  cylinder  when  the  piston  is 
withdrawn,  but  closes  when  the 
piston  is  forced  in.  The  collar 
thus  serves  as  a  valve,  allowing 
the  air  to  flow  one  way  but  not  the  other.  The 
compressed  air  is  forced  through  the  tube  form- 
ing the  piston  rod,  and  the  check  valve  in  the 
tire  inlet  prevents  its  return. 

90.  The  Air  Pump.  —  The  air  pump  for  re- 
moving air  or  any  gas  from  a  closed  vessel  de- 
pends for  its  action  on  the  expansive  or  elastic 
force  of  the  gas.  The  first  air  pump  was  invented  by  Otto 
von  Guericke,  burgomaster  of  Magdeburg,  about  1650. 


FIGURE    75.  —  AIR 
COMPRESSOR. 


FIGURE 
76. -BICY- 
CLE PUMP. 


THE  AIR  PUMP 


77 


FIGURE 


77.  —  SIMPLE 
PUMP. 


AIR 


In  the  very  simplest  form  the  two  valves,  corresponding 

with  those  of  the  air  compressor,  are  worked  by  the  pressure 

of  the  air.     But  though  they  may 

be   made   of   oiled   silk  and   very 

light,  the  pressure  in  the  vessel  to 

be  exhausted  soon  reaches  a  lower 

limit  below  which  it  is  too  small 

to  open  the  valve  between  it  and 

the    cylinder    of    the    pump.     On 

this     account     automatic     valves, 

operated  mechanically,  are  in  use 

in  the  better  class  of  pumps. 

The  modern  pump  in  its  sim- 
plest form  is  shown  in  Fig.  77.  The  two  valves  are  oper- 
ated by  the  pressure  of  the  air ;  they  are  of  oiled  silk  so 
as  to  be  as  light  as  possible.  When 
the  piston  descends,  valve  Fin  the 
piston  opens  and  V  at  the  bottom 
of  the  cylinder  closes ;  the  reverse 
is  true  when  the  piston^  ascends. 
The  limit  of  exhaustion  is  reached 
when  the  elastic  force  of  the  rare- 
fied air  is  not  sufficient  to  open 
the  valves. 

Figure  78  shows  in  section  the  cylinder 
of  an  air  pump  iu  which  the  valves  are 
automatic.  A  piston  P,  with  a  valve  at 
S,  works  in  a  cylindrical  barrel,  commu- 
nicating with  the  outer  air  by  a  valve 
V  at  its  upper  end,  and  with  the  receiver 

FIGURE  78. AIR  PUMP.        to  be  exhausted  by  the  horizontal  tube  at 

the  bottom.     The  valve  S'  is  carried  by  a 

rod  passing  through  the  piston,  and  fitting  tightly  enough  to  be  lifted 
when  the  upstroke  begins.     The  ascent  of  the  rod  is  almost  immediately 


78 


MECHANICS   OF  FLUIDS 


arrested  by  a  stop  near  its  upper  end,  and  the  piston  then  slides  on 
the  rod  during  the  remainder  of  the  upstroke.     The  open  valve  S' 

allows  the  air  to  flow  from  the  vessel 
to  be  exhausted  into  the  space  below 
the  piston.  At  the  end  of  the  upstroke 
the  valve  S'  is  closed  by  the  lever 
shown  in  dotted  lines.  During  the 
downward  movement  the  valve  S  is 
open,  and  the  inclosed  air  passes 
through  it  into  the  upper  part  of  the 
cylinder.  The  ascent  of  the  piston 
again  closes  S ;  and  as  soon  as  the  air 
is  sufficiently  compressed,  it  opens  the 
valve  V  and  escapes. 
Each  complete 
double  stroke  re- 
moves a  cylinder  full 
of  air;  but  as  it  be- 
comes rarer  with 


FIGURE  79.  —  FOOTBALL 
RECEIVER. 


FlGURE  80-  ~ 
AFTER  AIR  IN 
~  P 

HAUSTED 


each  stroke,  the  mass  removed  each  time  is  less. 
91.   Experiments    with    the    Air    Pump. — 

1.   Expansibility  of  air. 

(a)  Football.  Fill  a  small  rubber  foot- 
ball half  full  of  air,  and  place  under  a  big 
bell  jar  on  the  table  of  the  air  pump 
(Fig.  79).  When  the  air  is  exhausted 
from  the  jar,  the  football  expands  until 
it  is  free  from  wrinkles  (Fig.  80).  A  toy  balloon  may 
be  substituted. 

(&)    Bolthead.     A  glass  tube  with  a  large  bulb  blown 
on  one  end  (Fig.  81)  is  known  as  a  bolthead.     The  stem 
passes  air-tight  through  the  cap  of  the  bell  jar,  and  dips 
below  the  surface  of  the  water  in  the  inner  vessel.     When 
the  air  is  exhausted  from  the  jar,  the  air  in  the  bolthead 
FIGURE    expands   and    escapes    in    bubbles   through    the   water. 
81. — BOLT-    Readmission  of  air  into  the  jar  restores  the  pressure, 
HEAD'  and  drives  water  into  the  bolthead.     Why? 

2.   Air  pressure,     (a)  Downward.     Wet  a  piece  of  parchment  paper, 
and  tie  it  tightly  over  the  mouth  of  a  glass  cylinder  (Fig.  82).    A 


EXPERIMENTS   WITH  THE  AIR  PUMP' 


79 


FIGURE  82.  —  BURSTING 
PARCHMENT  PAPER. 


sheet  of  stout  paper  may  be  pasted  over  the  cylinder  instead.  When 
the  air  is  exhausted,  the  paper  will  break  with  a  loud  report. 

(6)  The  vacuum 
fountain.  A  tall 
glass  vessel  has  an 
inner  jet  tube  which 
may  be  closed  on  the 
outside  with  a  stop- 
cock. Exhaust  the 
air,  place  the  open- 
ing into  the  jet  tube 
in  water,  and  open 
the  stopcock.  The 
water  is  forced  by 
atmospheric  pres- 
sure into  the  exhausted  tube  like  a  fountain 
(Fig.  83). 

(c)    Upward  pressure.     A  strong  glass  cyl- 
inder supported  on  a  tripod  is  fitted  with  a 
piston  (Fig.  84).     The  brass  cover  of  the 
FIGURE  83.  — VACUUM  cylinder  is  connected  with  the  air  pump  by 
FOUNTAIN.  v,.  ,       ,  , 

a  thick  rubber  tube. 

When  the  air  is  exhausted,  the  piston  is  lifted 
by  atmospheric  pressure,  and  carries  the  heavy 

attached  weight. 

(of)  The  Magdeburg  hemispheres. 

This  historical  piece  of  apparatus 

was  designed  by  Otto  von  Gue- 

ricke  to  exhibit  the  great  pressure 

of  the  atmosphere  (  Fig.  85) .    The 

lips  of  the  two  parts  are  accurately 

ground  to  make  an  air-tight  joint 

when    greased.     When   they  are 

,  i   .1        •     •         FIGURE  84.  —  LIFTING 

brought  together  and  the  air  is  WEIQHT  BY  PRESSURE  QF 

exhausted,   it    requires  consider-  ATMOSPHERE. 

able  force  to  pull  them   apart. 

—  M  AG^E-  The  original  hemispheres  of  von  Guericke  were  about  22 
BURG  HEMI-  in-  in  diameter,  and  the  atmospheric  pressure  holding 
SPHERES.  them  together  was  about  5600  Ib. 


80 


MECHANICS   OF  FLUIDS 


FIGURE  86.  —  THE 
BAROSCOPE. 


92.  Buoyancy  of  the  Air.  —  A  small  beam  balance  has 
attached  to  one  arm  a  hollow  closed  brass  globe ;   it  is 
counterbalanced  in  air  by  a  solid  brass  weight  on  the  other 
arm.     When  the  balance  is  placed  under  a  bell  jar,  and  the 

air  is  exhausted,  the  globe^  overbalances 
the  solid  weight  (Fig.  86). 

The  apparatus  just  described  is  called 
a  baroscope.  It  shows  that  the  atmos- 
phere exerts  an  upward  or  buoyant 
force  on  bodies  immersed  in  it;  that  is, 
the  principle  of  Archimedes  applies  to 
gases  as  well  as  to  liquids.  The  buoy- 
ancy or  lifting  effect  of  the  atmosphere 
is  equal  to  the  weight  of  the  air  dis- 
placed by  a  body.  Whenever  a  body  is 
less  dense  than  the  weights,  it  weighs 
more  in  a  vacuum  than  in  the  air. 

93.  Balloons  and  airships  also  illustrate  the  buoyancy 
of  the  air.     A  soap  bubble  and  a  toy  balloon  filled  with 
air  fall  because  they  are  heavier  than  the  air  displaced; 
but  if  filled  with  hydrogen  or  coal  gas,  they  rise  in  the  air. 
Their  buoyancy  is  greater  than  their  weight,  including 
the  inclosed  gas.     The  weight  of  a  balloon  with  its  car 
and  contents  must  be  less  than  that  of  the  air  displaced 
by  it.     The  essential  part  of  a  balloon  is  a  silk  bag,  var- 
nished to  make  it  air-tight ;  it  is  filled  either  with  hydro- 
gen or  with  illuminating  gas.     A  cubic  meter  of  hydrogen 
weighs  about  0.09  kg.,  a  cubic  meter  of  illuminating  gas, 
0.75   kg.,  while  a  cubic  meter   of   air  weighs  1.29  kg. 
With  hydrogen  the  buoyancy  is  1.29  —  0.09  =  1.2  kg.  per 
cubic   meter;    with    illuminating    gas   it   is   1.29  —  0.75 
=  0.54  kg.  per  cubic  meter.     The  latter  is  more  commonly 
used  because  it  is  much  cheaper. 


BALLOONS 


81 


A  balloon  is  not  fully  inflated  to  start  with,  but  it 
expands  as  it  rises-  because  the  pressure  of  the  air  on 
the  outside  diminishes.  The  buoyancy  then  decreases 
slowly  as  the  balloon  ascends  into  a  rarer  atmosphere.  If 
it  were  fully  inflated  at  the  start,  the  inside  pressure  of 


THE  BRITISH  AIRSHIP  R  34. 

This  was  the  first  airship  to  cross  the  Atlantic.     It  is  shown  here  at  its 
moorings  on  Long  Island, 

the  gas  at  a  high  altitude  would  be  greater  than  the  out- 
side atmospheric  pressure,  and  the  bag  would  burst. 

Airships  are  balloons  with  steering  and  propelling  de- 
vices attached.  They  are  made  of  large  volume  so  as  to 
give  them  considerable  lifting  force.  Huge  Zeppelins 
have  been  made  775  feet  long,  and  holding  32,000  cubic 
feet  of  gas.  They  are  driven  by  several  gasoline  engines 
aggregating  from  4000  to  5000  horsepower.  Figure  87 


82  MECHANICS  OF  FLUIDS 

is  a  picture  of  a  Zeppelin  with  the  outer  rubberized 
cotton  cloth  D  partly  cut  away,  to  show  the  gas  balloons 
inside.  G-Q-  are  propellers,  shown  also  in  the  front  view 
in  the  corner  of  the  picture.  The  balancing  planes  and 
the  rudder  may  be  seen  at  the  rear  end. 


FIGURE  87. —  A  ZEPPELIN. 

Problems  and  Questions 

1.  What  limits  the  height  to  which  a  balloon  will  ascend? 

2.  A  pound  of  feathers  exactly  counterpoises  a  pound  of  shot  on 
the  scale  pans  of  a  balance.     Do  they  represent  equal  masses  of  mat- 
ter ?     Explain. 

3.  What  force  will  be  required  to  separate  a  pair  of  Magdeburg 
hemispheres,  assuming  the  air  to  be  entirely  removed  from  the  inside, 
the  diameter  of  the  hemispheres  being  4  in.  and  the  height  of  the 
barometer  30  in.  ? 

4.  The  volume  of  hydrogen  collected  over  mercury  in  a  graduated 
cylinder  was  50  crn.8,   the   mercury  standing  15  cm.  higher  in  the 
cylinder  than  outside  of  it.     The  reading  of  the  barometer  was  75 
cm.     How  many  cubic  centimeters  of  hydrogen  would  there  be  at  a 
pressure  of  76  cm.  ? 

SUGGESTION.  The  height  of  the  mercury  in  the  cylinder  above  the  surface 
of  the  mercury  outside  must  be  subtracted  from  the  barometer  reading  to  get 
the  pressure  of  the  gas  in  the  cylinder. 


THE  SIPHON  83 

5.  A  test  tube  is  forced  down  into  water  with  its  open  end  down, 
until  the  air  in  it  is  compressed  into  the  upper  half  of  the  tube. 
How  deep  down  is  the  tube  if  the  barometer  stands  at  30  in.  ?     (The 
specific  gravity  of  mercury  may  be  taken  as  13.6.) 

6.  With  what  volume  of  illuminating  gas  must  a  balloon  be  filled 
in  order  to  rise,  if  the  empty  balloon  and  its  contents  weigh  540  kg.  ? 

7.  A  mass  of  iron,  density  7.8,  weighs  2  kg.  in  air.     How  much 
will  it  weigh  in  a  vacuum  ? 

VL   PNEUMATIC  APPLIANCES 

94.  The  Siphon. — The  siphon  is  a  U-shaped  tube  em- 
ployed to  transfer  liquids  from  one  vessel  over  an  inter- 
vening elevation  to  another  at  a  lower, 
level  by  means  of  atmospheric  pressure. 
If  the  tube  is  filled  and  is  placed  in  the 
position  shown  in  Fig.  88,  the  liquid  will 
flow  out  of  the  vessel  and  be  discharged 
at  the  lower  level  D. 

If  the  liquid  flows  outward  past  the 
highest  point  of  the  tube  in  the  direction 
BO,  it  is  because  the  pressure  on  the 
liquid  outward  is  greater  than  the  pres- 
sure in  the  other  direction.  Now  the 
outward  pressure  at  the  top  is  the  pres- 
sure  of  the  atmosphere  transmitted  by 
the  liquid  to  the  top  minus  the  weight  FlGUI  ~  THE 
of  the  column  of  liquid  AB ;  while  the 
pressure  inward  is  the  atmospheric  pressure  transmitted 
to  the  top  by  the  liquid  in  BD  minus  the  weight  of  the 
column  DO.  Hence,  the  pressure  inward  is  less  than  the 
pressure  outward  by  the  weight  of  a  column  of  the  liquid 
equal  in  height  to  the  difference  between  AB  and  DO. 

AB  and  D(7are  the  lengths  of  the  arms  of  the  siphon. 
If  the  outer  arm  dips  into  the  liquid  in  the  receiving  vessel, 


MECHANICS   OF  FLUIDS 


the  arm  terminates  at  the  surface  of  the  liquid.  To  in- 
crease the  length  CD  is  to  increase  the  rate  of  flow.  As 
AB  and  D  C  approach  equality  the  rate  of  flow  decreases 
and  the  flow  ceases  when  this  difference  is  zero.  The 

siphon  fails  to  work  also 
when  B  is  about  33  feet 
above  A.  Why  ? 

On  a  small  scale  siphons 
are  used  to  empty  bottles  and 
carboys,  which  cannot  be 
tilted  to  pour  out  a  liquid; 
also  to  draw  off  a  liquid 
from  a  vessel  without  dis- 
turbing the  sediment  at  the 
bottom. 

On  a  large  scale  engineers 
have  used  siphons  for  drain- 
ing lakes  and  marshes;  also 
for  lifting  water  from  the 
ocean  or  other  large  body  of 
water  through  a  pipe  leading 
to  a  steam  condenser  in  a 
power  plant,  whence  it  flows 
back  through  the  return  pipe 
to  the  level  of  the  water 
supply.  The  pipes  are  con- 
tinuous and  air-tight,  and  the 
pump  has  no  work  to  do  ex- 
cept to  keep  the  water  run- 
ning against  friction  in  the 
pipes.  There  is  also  a  slight  back  pressure  because  the  water  on  the 
discharge  side  is  warmer  and  therefore  lighted  than  on  the  intake 
side. 

When  the  mains  of  a  water  supply  run  over  hills  to  a  lower  level, 
they  constitute  in  reality  siphons.  Air  is  carried  along  with  the 
water  and  collects  in  the  bends  at,  the  tops.  If  there  are  several  of 
these  siphons  one  after  another,  the  back  pressure  may  actually  stop 


SIPHON  OVER  A  MOUNTAIN. 
On  the  far  side  of  the  mountain  the  water 
is  lifted  by  gravity  pressure  to  within 
32  feet  of  the  top. 


THE  LIFT  PUMP 


85 


the  flow  of  water,  unless  the  air  is  removed  by  air 
pumps,  or  is  allowed  to  escape  under  pressure  through 
relief  valves. 

An  intermittent  siphon  (Fig.  89)  has  its  short  arm 
inside  a  vase  and  its  long  arm  passing  through  the 
bottom.  The  vase  will  hold  water  until  its  level 
reaches  the  top  of  the  bend  of  the  siphon.  It  then 
discharges  and  empties  the  vessel,  if  it  discharges 
faster  than  it  is  filled.  Again  the  water  rises  in  the 
vase,  and  the  siphon  again  emp- 
ties it.  Intermittent  springs  are 
supposed  to  operate  on  the  same 
principle. 

A  siphon  fountain  may  be  made  *  *  '  ^  K  w 
with  a  Florence  flask  and  glass  *~ 
tubing  (Fig.  90).  The  flask  is  partly  filled  with 
water,  and  the  apparatus  is  then  inverted  as  shown. 
The  water  enters  the  flask  as  a  jet.  If  a  piece 
of  rubber  tubing  is  attached  to  the  longer  arm,  the 
jet  will  rise  as  the  end  of  the  tubing  is  lowered. 
A  portion  of  the  water  runs  out  at  first,  producing 
a  partial  vacuum  inside. 
A  siphon  in  a  vacuum 
made  of  glass  tubing  about 
2  mm.  in  diameter  may  be 
set  up  with  mercury  as  the 
liquid.  If  it  is  set  in  action  under  a  tall  bell 
jar  on  the  air  pump,  it  will  stop  working  when 
the  air  is  exhausted  from  the  jar,  but  will  be- 
gin again  when  the  air  is  admitted. 

The  water  in  an  S-trap,  in  common  use  under 
sinks  and  washbowls,  may  be  siphoned  off  when 
the  discharge  pipe  is  filled  with  water  for  a 
short  distance  below  the  trap,  unless  the  trap 
is  ventilated  at  the  top  of  the  S.  Fig.  91 
shows  the  method  of  ventilating  such  traps. 

95.   The    Lift    Pump. -The  common  FrouRE  91._VENTILA. 
lift  or  suction  pump  acts  by  the  pres-       TION  OF  S-TRAP. 


-Vent  Pipe  to  Roof 


FIGURE  90.— SIPHON 
FOUNTAIN. 


First  Floor 


86 


MECHANICS   OF  FLUIDS 


sure  of  the  air  ;   it  is,  in  fact,  a  simple  form  of  air  pump ; 
but  it   was  in  use   2000  years  before  the  air  pump  was 

invented.  The  first  few  strokes 
serve  merely  to  draw  out  air  from 
the  pipe  below  the  valve  F  (Fig. 
92) ;  the  pressure  of  the  air  on 
the  water  in  the  well  or  cistern 
W,  then  forces  it  up  the  pipe 
$,  and  finally  through  the  valve 
V.  After  that,  when  the  piston 
descends,  the  valve  V 
closes  and  checks  the 
return  of  the  water, 
and  water  passes 
through  the  valve  V 
above  the  piston. 
The  next  upstroke 
lifts  the  water  to  the 

level  of  the  spout.  Since  the  pressure  of  the 
air  lifts  the  water  to  the  highest  point  to  which 
the  piston  ascends,  it  is  obvious  that  this  point 
cannot  be  more  than  the  limit  of  about  33  ft. 
above  the  water  in  the  well.  Practically  it  is 
less  on  account  of  leakage  through  the  imper- 
fect valves.  The  priming  of  a  pump  by  pour- 
ing in  a  little  water  to  start  it  serves  to  wet 
the  valves  and  make  them  air-tight. 

For  deep  wells  the  piston  rod  is  lengthened 
and  the  valves  v  and  v'  are  placed  far  down 
the  well ;  the  long  pump  rod  serves  to  lift  the  FIGURE  93. 
water  from  the  piston  to  the  spout  (Fig.  93).  -LIFT PUMP. 
96.  The  Force  Pump.  —  The  force  pump  (Fig.  94)  is 
used  to  deliver  water  under  pressure,  either  at  a  point 


FIGURE  92. —  SUCTION  PUMP. 


THE  AIR   BEAKS 


87 


FIGURE  94.  —  FORCE 


higher  than  the  pump  into  pipes,  as  in  the  fire  engine, 

into  boilers  against  steam  pressure,  or  into  the  cylinder 

of  the  hydraulic  press. 

The  air  dome  D  is  added  to  secure 

a  continuous  flow  through  the  delivery 

pipe   d.     Water   flows   out  through  vf 

only  while   the   piston   is   descending; 

without  the  air  dome,  therefore,  water 

would  flow  through   the   pipe   d   only 

during  the  downstroke  of  the  piston; 

but  the  water  under  pressure  from  the 

piston  enters  the  dome  and  compresses 

the  air.     The  elastic   force   of  the  air 

drives    the    water    out    again    as    soon 

as   v'  closes.     Thus  the   flow  is   practically  continuous. 
The  pump  of  a  steam  fire  engine  is  double  acting,  that 

is,  it  forces  water  out  while  the  piston  is  moving  in  either 

direction  (Fig.  95)  ;  so  also  are 
pumps  for  waterworks  and 
mines. 

97.  The  Air  Brake.  —  The  well- 
known  Westinghouse  air  brake  is  oper- 
ated by  compressed  air.  In  Fig.  96 
P  is  the  train  pipe  leading  to  a  large 
reservoir  at  the  engine  in  which  an 
air  compressor  maintains  a  pressure 
of  about  75  Ib.  per  square  inch.  So 
long  as  this  pressure  is  applied  through 
P,  the  automatic  valve  V  maintains 
communication  between  P  and  an  auxiliary  reservoir  R  under  each 
car,  and  at  the  same  time  shuts  off  air  from  the  brake  cylinder  C. 
But  as  soon  as  the  pressure  in  P  falls,  either  by  the  movement  of  a 
lever  in  the  engineer's  cab  or  by  the  accidental  parting  of  the  hose 
coupling  k,  the  valve  V  cuts  off  P  and  connects  the  reservoir  R  with 
the  cylinder  C.  The  pressure  on  the  piston  in  C  drives  it  powerfully 


FIGURE  95.  —  FIRE  ENGINE  PUMP. 


88 


MECHANICS   OF  FLUIDS 


to  the  left  and  sets  the  brake  shoes  against  the  wheels.     As  soon  as 
air  from  the   main  reservoir  is  again   admitted  to  the  pipe  P,  the 

valve  V  reestablishes  com- 
munication between  P  and 
R,  and  the  confined  air  in 
C  escapes.  The  brakes  are 
released  by  the  action  of 
the  spring  S  in  forcing  the 
piston  back  to  the  right. 

98.  Other  Applications 
of  the  Air  Pump  and  the 
Air  Compressor.  —  The 

air  pump  and  the  air  com- 
pressor are  extensively  used 

F.GURE  96.-A.R  BRAKE.  in  industry.    Sugar  refiners 

employ  the  air  pump  to  re- 
duce the  boiling  point  of  the  sirup  by  lowering  the  pressure  on  its  sur- 
face in  the  evaporating  pan ;  manufacturers  of  soda  water  use  a  com- 
pressor to  charge  the  water  with  carbon  dioxide ;  in  pneumatic  dispatch 


FIGURE  97.  —  RIVETING  HAMMER. 


tubes,  now  extensively  used  for  carrying  small  packages,  both  the  air 
pump  and  the  compressor  are  used,  one  to  exhaust  the  air  from  the 
tube  in  front  of  the  closely  fitting  carriage,  and  the  other  to  compress 
air  in  the  tube  behind  it,  so  as  to  propel  the  carriage  with  great 
velocity.  The  air  compressor  is  employed  to  make  a  forced  draft  for 


QUESTIONS  AND  PROBLEMS  89 

steam  boilers,  to  ventilate  buildings,  and  to  operate  machinery  in 
places  difficult  of  access,  as  in  mines,  where  it  furnishes  fresh  air  as 
well  as  power.  It  is  employed  also  in  the  pneumatic  caisson  for 
making  excavations  and  laying  foundations  under  water.  The  cais 
son  is  a  large  heavy  air  chamber  which  sinks  as  the  soft  earth  is 
removed  from  within.  When  its  bottom  is  below  water  level,  air  is 
forced  in  under  sufficient  pressure  to  prevent  the  entrance  of  water. 
Access  to  it  is  gained  by  air-tight  locks. 

Compressed  air  is  frequently  used  for  operating  railway  signals, 
and  to  control  automatic  heating  and  ventilating  appliances.  Pneu- 
matic tools  are  used  for  calking  seams  and  joints,  for  stone  cutting, 
chipping  iron,  and  riveting.  Figure  97  shows  a  riveting  hammer ; 
A  is  the  air  pipe,  B  the  trigger  for  controlling  the  air,  and  C  the 
hammer. 

The  vacuum  cleaner  is  essentially  a  fan  driven  by  an  electric  motor. 
The  fan  pushes  the  air  away  from  one  face  and  atmospheric  pressure 
forces  air  through  the  mouthpiece  of  a  tube  leading  to  the  fan  to  fill 
the  partial  vacuum.  This  stream  of  air  carries  with  it  the  dust  of 
the  rug  o»  carpet. 

Questions  and  Problems 

1.  What  will  happen  if  the  tip  of  an  incandescent  lamp  bulb  be 
broken  off  under  water? 

2.  How  can  a  tumbler  of  water  be  inverted  (with  the  aid  of  a 
card)  without  spilling  the  water? 

3.  Explain  why  the  "  priming  "  of  a  dry  suction  pump  restores  it 
to  working  condition. 

4.  What  sort  of  rubber  tube  must  be  used  to  connect  a  receiver 
to  be  exhausted  by  an  air  pump  ? 

5.  What  is  the  limit  of  pressure  to  which  a  large  suction  water 
pump  can  subject  the  intake  pipe?     Will   the  pipe   collapse  if  the 
pump  "sucks"  hard  enough? 

6.  When  the  barometer   stands   at  29  in.,  what  is  the  limiting 
height  over  which  a  siphon  can  carry  water  ? 

7.  A  vessel  36  in.  deep  is  filled  with  mercury;   can  it  be  com- 
pletely emptied  by  means  of  a  siphon  ? 


90  MECHANICS  OF  FLUIDS 

8.  A  diver  works  in  35  feet  of  sea  water,  specific  gravity  1.025 
What  pressure  must  the  compression  pump  supply  to  counterbalance 
the  water  pressure  ? 

9.  When  the  barometer  reading  is  73  cm.,  what  is  the  greatest 
possible  length  of  the  short  arm  of  a  siphon  when  used  for  sulphuric 
acid,  density  1.84  g.  per  cubic  centimeter? 

10.   If  the  pressure  against  the  8  in.  piston  of  an  air  brake  is  80  Ib. 
per  square  inch,  what  is  the  force  driving  the  piston  forward  ? 


CHAPTER  IV 

MOTION 
I.   MOTION  IN  STRAIGHT  LINES 

99.  All  Motion  Relative.  —  Rest  and  motion  are  relative 
terms  only.     A  body  is  at  rest  when  its  relative  position 
with  respect  to  some  point,  line,  or  surface  remains  un- 
changed ;  but  when  that  relative  position  is  changing,  the 
body  is  in  motion. 

The  moving  about  of  a  person  on  a  ship  is  relative  to  the  vessel; 
the  movement  of  the  ship  across  the  ocean  is  relative  to  the  earth's 
surface ;  the  daily  motion  of  the  earth's  surface  is  relative  to  its  axis 
of  rotation  ;  the  motion  of  the  earth  as  a  whole  is  relative  to  the  sun ; 
while  the  sun  itself  is  drifting  with  other  stars  through  space. 

100.  Types  of  Motion.  —  Many  familiar  motions  are  irreg- 
ular in  every  way,  both  as  to  direction  and  speed.     The 
flight  of  a  bird,  the  running  of  a  boy  at  play,  and  even 
the  motion  of  a  man  riding  a  horse,  are  illustrations.     We 
shall  study  only  those  motions  that  can  be  classified  and 
reduced  to  simple  terms. 

The  line  described  by  a  moving  body  is  its  path.  When 
this  path  is  straight,  like  that  of  a  falling  body,  the  motion 
is  rectilinear ;  when  it  is  a  curved  line,  like  that  of  a 
rocket,  the  motion  is  curvilinear. 

Then  there  is  also  simple  harmonic  motion,  exemplified 
by  the  to-and-fro  swing  of  a  pendulum  ;  and  rotary  motion 
about  an  axis,  such  as  the  rotation  of  the  earth  on  its  axis, 
and  that  of  the  pulley  and  armature  of  a  stationary  elec- 

91 


92 


MOTION 


trie  motor.  The  motion  of  a  carriage  wheel  along  a  level 
road,  and  that  of  a  ball  along  the  floor  of  a  bowling  alley 
combine  motion  of  rotation  with  rectilinear  motion. 

101.  Speed  or  Velocity.  —  If  an  automobile  runs  thirty 
miles  in  an  hour  and  a  half,  its  average  speed  is  20  miles 
per  hour.  Speed  or  velocity  is  the  rate  of  motion,  that  is, 
it  is  the  distance  traversed  per  unit  of  time.  In  express- 
ing a  speed  or  a  velocity  the  time  unit  must  be  given  as 


THE  TWENTIETH  CENTURY  LIMITED  AT  SIXTY  MILES  AN  HOUR. 
The  railway  train  is  one  of  our  most  familiar  examples  of  motion. 

well  as  the  numerical  value.  Thus,  60  miles  per  hour, 
5280  feet  per  minute,  and  26.82  meters  per  second  are  all 
expressions  for  the  same  speed. 

There  is  but  little  distinction  between  speed  and  ve- 
locity. Both  express  the  rate  of  motion,  but  velocity  is 
generally  used  to  express  the  rate  of  motion  in  a  definite 
direction,  while  speed  is  rate  of  motion  without  reference 
to  direction. 

102.  Uniform  Motion.  —  If  the  motion  is  over  equal  dis- 
tances in  equal  and  successive  units  of  time,  the  motion  is 
uniform  and  the  velocity  is  constant.  In  uniform  motion 


ACCELERATION  98 

the  whole  distance  traversed  is  found  by  multiplying  the 
speed  by  the  time,  or 

distance  =  speed  x  time. 
In  symbols  this  is  written,  s  =  v  x  t ;  from  which 

v  =  -  and  t  =  -    .     .     (Equation  4) 
t  v 

EXAMPLE.  A  railway  train  runs  uniformly  covering  660  ft.  in 
10  min.  Then  the  speed  v  =  6T6<£  —  66  ft.  per  minute,  or  £  mi.  per 
hour.  The  distance  s  =  66  x  10  =  660  ft.  The  time  t  =  6g6^  =  10  min. 

The  average  speed  in  variable  motion  is  found  in  the 
same  way  as  in  uniform  motion,  namely,  by  dividing  the 
space  traveled  by  the  time. 

103.  Velocity  at  any  Instant.  —  When  the  motion  is  vari- 
able, the  velocity  of  a  body  at  any  instant  is  the  distance 
it  would  travel  in  the  next  unit  of  time  if  at  that  instant 
its  motion  were  to  become  uniform. 

For  example :  The  velocity  of  a  falling  body  at  any 
moment  is  the  distance  it  would  fall  during  the  following 
second,  if  the  attraction  of  the  earth  and  the  resistance  of  the 
air  were  both  to  be  withdrawn.  The  velocity  of  a  ball  as  it 
leaves  the  muzzle  of  a  gun  is  the  distance  it  would  pass 
over  in  the  second  following  if  from  that  instant  it  should 
continue  to  move  for  a  second  without  any  change  in  speed. 
Actually  the  motion  of  the  body  and  the  ball  for  the  suc- 
ceeding second  is  variable  ;  the  question  is,  what  would  be 
the  velocity  if  the  motion  were  invariable  ? 

104.  Acceleration.  —  When  a  train  runs  a  mile  a  minute 
for  several  minutes,  it  moves  with  uniform  velocity ;  but 
when  it  is  starting  or  slowing  down,  it  is  said  to  be  accel- 
erated.    If  the  velocity  increases,  the  acceleration  is  posi- 
tive; if  it  decreases,  it  is  negative.     A  falling  body  goes 


94  MOTION 

faster  and  faster  ;  it  has  a  positive  acceleration.  A  body 
thrown  upward  goes  more  and  more  slowly ;  it  has  a 
negative  acceleration.  A  loaded  sled  starts  from  rest  at 
the  top  of  a  long  hill ;  it  gains  in  velocity  as  it  descends 
the  hill ;  it  has  a  positive  acceleration.  When  it  reaches 
the  bottom,  it  loses  velocity  and  is  retarded,  or  has  a 
negative  acceleration,  until  it  stops.  Acceleration  is  the 
rate  of  change  of  speed. 

Acceleration  =  change  in  speed  per  unit  time. 

Acceleration  is  always  expressed  as  so  many  units  of 
speed  per  unit  of  time.  If,  for  example,  a  street  car  start- 
ing from  rest  gains  uniformly  in  speed,  so  that  at  the  end 
of  ten  seconds  it  has  a  speed  of  10  miles  per  hour,  its  ac- 
celeration is  its  gain  in  speed-per-hour  acquired  in  one 
second,  or  1  mile-per-hour  per  second. 

105.  Uniform  Acceleration.  — If  the  change  in  velocity  is 
the  same  from  second  to  second,  the  motion  is  uniformly 
accelerated.  The  best  example  we  have  of  uniformly  ac- 
celerated motion  is  that  of  a  falling  body,  such  as  a  stone 
or  an  apple.  Neglecting  the  resistance  of  the  air,  its  gain 
in  velocity  is  9.8  m.-per-second  for  every  second  it  falls. 
Its  acceleration  is  therefore  9.8  m.-per-second  per  second ; 
in  other  words,  it  gains  in  velocity  9.8  m.-per-second  for 
every  second  of  time.  This  is  equivalent  to  an  increase  in 
velocity  of  588  m.-per-second  acquired  in  a  minute  of  time. 
The  unit  of  time  enters  twice  into  every  expression  for 
acceleration,  the  first  to  express  the  change  in  velocity, 
and  the  second  to  denote  the  interval  during  which  this 
change  takes  place. 

If  an  automobile  starts  from  rest  and  increases  its  speed  one  foot  a 
second  for  a  whole  minute,  its  velocity  at  the  end  of  the  minute  is 
60  ft.  per  second.  Since  it  gains  in  one  second  a  velocity  of  one  foot 


DISTANCE  TRAVERSED  95 

a  second,  and  in  one  minute  a  velocity  of  60  ft.  a  second,  its  accelera- 
tion may  be  expressed  either  as  one  foot-per-second  per  second,  or  as 
60  ft.-per-second  per  minute.  Its  velocity  is  constantly  changing ;  its 
acceleration  is  constant. 

106.  Velocity  in  Uniformly  Accelerated  Motion.  —  Suppose 
a  body  to  move  from   rest  in  any  given  direction  with  a 
constant  acceleration  of  5  ft.-per-second  per  second.     Its 
velocity  at  the  end  of  the  first  second  will  be  5  ft.  per 
second ;  at  the  end  of  two  seconds,  2  x  5  ft. ;  at  the  end 
of  three  seconds,  3  x  5  ft. ;  and  at  the  end  of  t  seconds, 
t  x  5  ft.  per  second ;  that  is, 

final  velocity  =  time  x  acceleration, 

or  in  symbols,  . 

v  =  ta  ;  whence  a  =  -.     .     (Equation  5) 
Hence, 

In  uniformly  accelerated  motion  the  speed  acquired  in 
any  given  time  is  proportional  to  the  time. 

107.  Distance  traversed  in  Uniformly  Accelerated  Motion.  — 

If  we  can  find  the  mean  or  average  velocity  for  any 
period  of  t  seconds,  the  distance  s  traversed  in  t  seconds 
may  be  found  precisely  as  in  the  case  of  uniform  motion 
(§  102).  For  a  body  starting  from  rest  with  an  accelera- 
tion of  5  feet-per-second  per  second,  for  example,  its  ve- 
locity at  the  end  of  four  seconds  is  4  x  5  ft.  per  second,  and 
the  average  velocity  for  the  four  seconds  is  the  mean  be- 
tween 0  and  4  x  5,  or  2  x  5  ft.  per  second,  the  velocity  at 
the  middle  of  the  period.  So  at  the  end  of  t  seconds  the 
average  velocity  is  \  ta  ft.  per  second.  Then  we  have 

distance  =  average  velocity  x  time, 


96  MOTION 

or  in  symbols,  s  =  %taxt  =  \at\     .     (Equation  6) 

Hence, 

In  uniformly  accelerated  motion  the  distance  traversed 
from  rest  is  proportional  to  the  square  of  the  time. 

108.  Uniformly  Accelerated  Motion  Illustrated. — The  old- 
est method  of  demonstrating  uniformly  accelerated  motion 

was  devised  by 
Galileo.  It  con- 
sists of  an  inclined 
plane  two  or  three 
meters  long  (Fig. 
98),  made  of  a 
straight  board  with 
a  shallow  groove, 

down  which  a  mar- 

FIGURE  98.  —  GALILEO'S  INCLINED  PLANE. 

ble  or  a  steel  ball 

may  roll  slowly  enough  to  permit  the  distances  to  be  noted. 
For  measuring  time,  a  clock  beating  seconds,  or  a  metro- 
nome, may  be  used.  Assume  a  metronome  as  shown  in 
the  figure  adjusted  to  beat  seconds.  One  end  of  the  board 
should  be  elevated  until  the  ball  will  roll  from  a  point  near 
the  top  to  the  bottom  in  three  seconds. 

Hold  the  ball  in  the  groove  against  a  straightedge  in 
such  a  way  that  it  may  be  quickly  released  at  a  click  of 
the  metronome.  Find  the  exact  position  of  the  straight- 
edge near  the  top  of  the  plane  from  which  the  ball  will 
roll  to  the  bottom  and  strike  the  block  there  so  that  the 
blow  will  coincide  with  the  third  click  of  the  metronome 
after  the  release  of  the  ball.  Measure  exactly  the  dis- 
tance between  the  upper  edge  of  the  straightedge  and  the 
block  at  the  bottom  and  call  it  9  d.  Next,  since  distances 
are  proportional  to  the  square  of  the  times,  let  the  straight- 


UNIFORMLY  ACCELERATED  MOTION 


97 


edge  be  placed  at  a  distance  of  4d  from  the  block;  the 
ball  released  at  this  point  should  reach  the  block  at  the 
second  click  of  the  metronome  after  it  starts.  Finally, 
start  the  ball  against  the  straightedge  at  a  distance  d 
from  the  block;  the  interval  this  time  should  be  that  of 
one  beat  of  the  metronome. 


TABULAR  EXHIBIT 


NUMBER  OF 
BEATS,  t 

WHOLE  DISTANCE 
FALLEN,  * 

DISTANCE  IN  SUCCES- 
SIVE INTERVALS 

VELOCITIES 
ATTAINED,  * 

I 

d 

d 

2d 

2 

±d 

3d 

4d 

3 

9d 

5d 

Qd 

4 

IQd 

Id 

8d 

The  third  column  is  derived  by 
subtracting  the  successive  numbers 
of  the  second.  To  get  the  fourth 
column,  we  notice  that  if  t  is  one 
second  in  Equation  6,  then  «  =  \  a\ 
that  is,  the  distance  traversed  in 
the  first  second  is  one  half  the  accel- 
eration. But  the  acceleration  is 
the  same  as  the  velocity  acquired 
the  first  second.  Hence  s  =  J  v 
and  d  =  J  v.  Therefore  the  veloc- 
ity at  the  end  of  the  first  second 
on*  the  inclined  plane  is  2  d.  Since 
by  Equation  5  the  velocities  are 
proportional  to  the  time,  the  suc- 
ceeding velocities  are  4  d,  6  df,  etc.  ^.=8d7"; 

The    numbers    in    the    second 


3d 


4.d 


FIGURE  99.  —  LAWS  OF  FALL- 
ING BODIES. 


98  MOTION 

column  show  that  the  distances  traversed  are  proportional 
to  the  squares  of  the  time  [compare  Equation  6] ;  those 
of  column  three  show  that  the  distances  in  successive 
seconds  are  as  the  odd  numbers  1,  3,  5,  etc.  The  results 
are  shown  graphically  in  Fig.  99. 

Problems 

NOTE.    For  the  relation  between  the  circumference  of  a  circle  and  its 
diameter,  see  the  Mensuration  Table  in  the  Appendix. 

1.  An  aviator  drives  his  aeroplane  through  the  air  a  distance  of 
500  km.  in  8  hr.  20  min.     What  was  his  average  speed  per  minute? 

2.  The  engine  drives  a  boat  downstream  at  the  rate  of  15  mi.  an 
hour,  while  the  current  runs  3  ft.  a  second.     How  long  will  it  take  to 
go  50  mi.? 

3.  A   man  runs  a  quarter  of  a  mile  in  48.4  seconds.     At  that 
speed,  what  was  his  time  for  100  yd.? 

4.  If  a  man  can  run  100  yd.  in  10  sec.,  what  would  be  his  time  for 
a  mile,  if  it  were  possible  to  maintain  the  same  speed? 

5.  A  procession  100  yd.  long,  moving  at  the  rate  of  3  mi.  an  hour, 
passes  over  a  bridge  120  yd.  long.     How  long  does  it  take  the  proces- 
sion to  pass  entirely  over  the  bridge  ? 

6.  An  express  train  is  running  60  mi.  an  hour.     If  the  train  is 
500  ft.  long,  how  many  seconds  will  it  be  in  passing  completely  over  a 
viaduct  160  ft.  in  length  ? 

7.  A  locomotive  driving  wheel  is  2  m.  in  diameter.     If  it  makes 
200  revolutions  per  minute,  what  is  the  speed  of  the  locomotive  in 
kilometers  per  hour,  assuming  no  slipping  of  the  wheel  on  the  track? 

8.  An  automobile  running  at  a  uniform  speed  of  25  mi.  per  hour 
is  10  mi.  behind  another  one  on  the  same  highway  running  20  mi.  per 
hour.     How  long  will  it  take  the  former  to  overtake  the  latter,  and 
how  far  will  each  machine  have  gone  during  this  time  ? 

9.  If  the  acceleration  of  a  marble  rolling  down  an  inclined  plane 
is  40  cm.-per-second  per  second,  what  will  be  its  velocity  after  3  sec. 
from  rest  ? 

10.   How  far  will  a  marble  travel  down  an  inclined  plane  in  3  sec. 
if  the  acceleration  is  40  cm.-per-second  per  second? 


DIRECTION  OF  MOTION  ON  A   CURVE  99 

11.  A  body  starts  from  rest,  and  moving  with  uniformly  acceler- 
ated  motion    acquires  in  10  sec.  a  velocity  of  3600  m.  per  minute. 
What  is  the  acceleration  per-second  per  second.     How  far  does  the 
body  go  in  10  sec.  ? 

12.  What  acceleration  per-minute  per  minute  does  a  body  have  if 
it  starts  from  rest  and  moves  a  distance  of  a  mile  in  5  min.?    What 
will  be  its  velocity  at  the  end  of  4  minutes  ? 

13.  If  a  train  acquires  in  2  min.  a  velocity  of  60  mi.  an  hour,  what 
is  its  acceleration  per-minute  per  minute,  assuming  uniformly  accel- 
erated motion  ? 

14.  An  electric  car  starting  from  rest  has  uniformly  accelerated 
motion  for  3  rnin.     At  the  end  of  that  time  its  velocity  is  27  km.  an 
hour.     What  is  its  acceleration  per-minute  per  minute  ? 

15.  A  sled  is  pushed  along  smooth  ice  until  it  has  a  velocity  of  4 
m.  per  second.     It  is  then  released  and  goes  100  m.  before  it  stops. 
If  its  motion  is  uniformly  retarded,  what  is  the  retardation  in  centi- 
meters-per -second  per  second  ? 

16.  To  acquire  a  speed  of  60  mi.  an  hour  in  10  min.,  how  far  would 
an   express  train  have  to  run,  provided  it  started  from  rest  and  its 
motion  were  uniformly  accelerated  ? 

II.   CURVILINEAR  MOTION 

109.   Direction  of  Motion  on  a  Curve.  —  Curvilinear  motion, 
or  motion  along  a  curved  line,  occurs  more  frequently  in 
nature  than  motion  in  a  straight  line.     The  motion  of  a 
point  on  the  earth's  surface  and  about 
its  axis  is  in  a  circle;  the  motion  of 
the  earth  in  its  path  around  the  sun 
is  along  a  curve  only  approximately 
circular;  the  motion  of  a  rocket  or  of 
a  stream  of  water  directed  obliquely 
upward  is   along  a  parabolic  curve. 
So  also  is  the  motion  of  a  baseball 
when  batted  high  in  air.     The  thrown 
"  curved  ball,"  too,  illustrates  curvi-     FIGURE  100.  —  MOTION 
linear  motion.  ALONG  A  CURVE. 


100  MOTION 

When  the  motion  is  along  a  curved  line,  the  direction 
of  motion  at  any  point,  as  at  B  (Fig.  100),  is  that  of  the 
line  CD,  tangent  to  the  curve  at  the  point.  This  is  the 
same  as  the  direction  of  the  curve  at  the  point. 

110.  Uniform  Circular  Motion.  — In  uniform  circular  mo- 
tion the  velocity  of  the  moving  body,  measured  along  the 
circle,  is  constant.  There  is  then  no  acceleration  in  the 
direction  in  which  the  body  is  going  at  any  point.  But 
while  the  velocity  remains  unchanged  in  value,  it  varies  in 
direction.  If  a  body  is  moving  with  constant  velocity  in 
a  straight  line,  its  acceleration  is  zero  in  every  direction; 
but  if  the  direction  of  its  motion  changes  continuously,  then 
there  is  an  acceleration  at  right  angles  to  its  path  and  its 
motion  becomes  curvilinear.  If  this  ac- 
celeration is  constant,  the  motion  is  uni- 
form in  a  circle.  Hence,  in  uniform 
circular  motion  there  is  a  constant  acceler- 
ation directed  toward  the  center  of  the 
circle.  It  is  called  centripetal  accelera- 
tion. 

FIGURE  101.  — CEN-  Uniform  circular  motion  consists  of  a 
TRIPETAL  ACC^LERA-  uniform  motion  in  the  circumference  of 
the  circle  and  a  uniformly  accelerated 
motion  along  the  radius.  If  v  is  the  uniform  velocity 
around  the  circle  whose  radius  is  r,  the  value  of  the  cen- 
tripetal acceleration  is 

v2* 
a= — ,     ....     (Equation  7) 

.   .     .  7         7      ^  •          square  of  velocity  in  circle 

or  centripetal  acceleration  =  -^ *- Jt 

radius  of  circle 


* Let  ABC  (Fig.  101)  be  the  circle  in  which  the  body  revolves,  and 
AB  the  minute  portion  of  the  circular  path  described  in  a  very  small 
interval  of  time  t.  Denote  the  length  of  the  arc  AB  by  s.  Then,  since 


MOTION  AND  FORCE. 

Above  :  White  Star  Liner  "  Britannic." 

Below :  Part  of  Boston  Elevated  Company's  Power  Plant. 


SIMPLE  HARMONIC  MOTION    >  101 


III.   SIMPLE  HARMONIC  MOTION 

111.  Periodic  Motion.  —  The  motion  of  a  body  is  said  to 
be  periodic  when  it  goes  through  the  same  series  of  move- 
ments in  successive  equal  periods  of  time.     It  is  vibratory 
if  it  is  periodic  and  reverses  its  direction  of  motion  at  the 
end  of  each  period.     The  motion  of  the  earth  around  the 
sun  is  periodic,  but  not  vibratory.     A  hammock  swinging 
in  the  wind,  the  pendulum  of  a  clock,  a  bowed  violin 
string,  and  the  prong  of  a  sounding  tuning 

fork  illustrate  both  periodic  and  vibratory 
motion. 

112.  Simple  Harmonic  Motion.  —  Suspend  a 
ball  by  a  long  thread  and  set  it  swinging  in  a  hori- 
zontal circle  (Fig.  102).     Place  a  white  screen  back 
of  the  ball  and  a  strong  light,  such  as  an  arc  light  or 
a    Welsbach 

gas  light,  at 

T-r 

a  distance  of  JL 
twelve  or  fif- 
teen  feet  in 
front  and  on  a  level  with  the  ball.     Viewed  in 

darkened  room,  a  shadow  of  the  ball  will  be  seen  FIGURE    102. SIMPLE 

on  the  screen,  moving  to  and  fro  in  a  straight      HARMONIC  MOTION. 
line.     This  motion  is  very  nearly  simple  harmonic 

and  would  be  perfectly  so  if  the  projection  could  be  made  with  sun- 
light, so  that  the  projecting  rays  were  perpendicular  to  the  screen. 


the  motion  along  the  arc  is  uniform,  s  =  vt.  AB  is  the  diagonal  of  a  very 
small  parallelogram  with  sides  AD  and  AE.  The  latter  is  the  distance 
through  which  the  revolving  body  is  deflected  toward  the  center  while 
traversing  the  very  small  arc  AB.  Since  the  acceleration  is  constant, 
AE  =  \  at2  by  Equation  6.  The  two  triangles  ABE  and  ABC  are  simi- 
lar. Hence  AB2  —  AE  x  AC.  Calling  the  radius  of  the  circle  r  and 
substituting  for  AB,  AE,  and  AC  their  values,  vW  =  |a£2  x  2r  =  at*r. 

Then  a  =  -• 


102 


MOTION 


Simple  harmonic  motion  is  the  projection  of  a  uniform  cir- 
cular motion  on  a  straight  line  in  the  plane  of  the  circle. 
All  pendular  motions  of  small  arc  are  simple  harmonic. 
The  name  appears  to  be  due  to  the  fact  that  simple  musical 
sounds  are  caused  by  bodies  vibrating  in  this  manner. 

The  graph  of  a  simple  harmonic  motion  is  obtained  as  follows : 
Draw  the  circle  adgk  (Fig.  103)  representing  the  path  of  the  ball,  and 
the  straight  line  ADG  its  projection  on 
the  screen.  Divide  the  circumference  into 
any  even  number  of  equal  parts,  as  twelve. 
Through  the  points  of  division  let  fall  per- 
pendiculars on  AG,  as  aA,  bB,  cC,  etc. 
Now  as  the  ball  moves  along  the  arc  adg, 
its  shadow  appears  to  the  observer  to 
move  from  A  through  B,  C,  etc.,  to-  G, 
where  it  momentarily  comes  to  rest.  It 
then  starts  back  toward  A,  at  first  slowly, 
but  with  increasing  velocity  until  it  passes 
D.  Its  velocity  then  decreases,  and  at  A 
it  is  again  zero,  and  its  motion  reverses. 


c 


D 


FIGURE  103.  —  GRAPH  SIMPLE 
HARMONIC  MOTION. 


The  radius  of  the  circle,  or  the  distance  AD,  is  the 
amplitude  of  the  vibration.  The  period  of  the  motion  is  the 
time  taken  by  the  ball  to  go  once  around  the  circle  ;  it  is 
the  same  as  the  time  of  a  double  oscillation  of  the  projected 
motion.  The  frequency  of  the  vibration  is  the  reciprocal 
of  the  period.  For  example,  if  the  period  is  J  a  second, 
the  frequency  is  2,  that  is,  two  complete  vibrations  per 
second.  This  relation  finds  frequent  illustration  in  musi- 
cal sounds,  where  pitch  depends  on  the  frequency  ;  in 
light,  where  frequency  determines  the  color ;  and  in  alter- 
nating currents  of  electricity,  where  a  frequency  of  50,  for 
example,  means  that  a  complete  wave  is  produced  every 
fiftieth  of  a  second,  and  that  the  current  reverses  100  times 
per  second. 


PROBLEMS  103 

Two  simple  harmonic  motions  of  the  same  period  are 
said  to  differ  in  phase  when  they  pass  through  their 
maximum  or  minimum  velocities  at  a  different  time.  Thus, 
if  one  has  its  maximum  velocity  at  the  same  instant  that 
the  other  has  its  minimum,  the  two  motions  differ  in  phase 
by  a  quarter  of  a  period. 

Problems 

1.  At  what  speed  must  an  automobile  be  driven  to  go  four  times 
around  a  circular  track  one  mile  in  diameter  in  thirty  minutes? 

2.  The  equatorial   diameter  of  the   earth  is   about  8000   miles. 
What  is  the  speed  in  miles  per  minute  of  a  point  on  the  equator, 
owing  to  the  earth's  rotation  on  its  axis  ? 

3.  A  conical  pendulum  swinging  in  a  circle  whose  diameter  is  50 
cm.  makes  5  complete  revolutions  in  15  seconds.     What  is  the  centrip- 
etal acceleration  of  the  bob  ? 

4.  The  radius  of  the  moon's  orbit  is  240,000  miles,  and  the  moon 
revolves  around  the  earth  in  27  days,  8  hours.     What  is  its  centripetal 
acceleration  with  respect  to  the  earth  in  f eet-per-second  per  second  ? 

5.  A  balance  wheel  on  a  stationary  engine  is  10  ft.  in  diameter  and 
makes  100  revolutions  per  minute.      A  point  on  its  circumference  has 
what  centripetal  acceleration  per-second  per  second  ? 

6.  The  earth's  equatorial  radius  is  20,926,000  feet,  and  the  period 
of  the  earth's  rotation  on  its  axis  is  23  h.,  56  min.,  4  sec.     Calculate  the 
the  centripetal  acceleration  per-second  per  second  at  the  equator. 


CHAPTER   V 

MECHANICS   OF   SOLIDS 
I.   MEASUREMENT  OF  FORCE 

113.  Force.  — A  preliminary  definition  of  force  as  a  push 
or  a  pull  has  already  been  given.  The  effects  of  force  in 
producing  motion  are  among  our  commonest  observations. 


A  BRITISH  "TANK"  GOING  INTO  ACTION. 
The  "  tank  "  exerts  enough  force  to  break  down  trees  and  walls. 

A  brick  loosened  from  a  chimney  or  pushed  from  a  scaffold 
falls  by  the  force  of  gravity  ;  a  mountain  stream  rushes 
down  by  reason  of  the  same  force  in  nature;  the  leaves  of 
a  tree  rustle  in  the  breeze,  the  branches  sway  violently  in 
the  wind,  and  their  trunks  are  even  twisted  off  by  the 

104 


UNITS   OF  FORCE  105 

force  of  the  tornado;  powder  explodes  in  a  rifle  and  the 
bullet  speeds  toward  its  mark;  loud  thunder  makes  the 
earth  tremble  and  vivid  lightning  rends  a  tree  or  shatters 
a  flagstaff.  From  many  such  familiar  facts  is  derived  the 
conception  that  force  is  anything  that  produces  motion  or 
change  of  motion  in  material  bodies.  It  remains  now  to 
explain  how  force  is  measured. 

114.  Units  of  Force.  —  Two  systems  of  measuring  force 
in  common  use  are  the  gravitational  and  the  absolute.  The 
gravitational  unit  of  force  is  the  weight  of  a  standard  mass, 
such  as  the  pound  of  force,  the  gram  of  force,  or  the  kilo- 
gram of  force.  A  pound  of  force  means  one  equal  to  the 
force  required  to  lift  the  mass  of  a  pound  against  the  down- 
ward pull  of  gravity.  The  same  is  true  of  the  metric 
units  with  the  difference  in  the  mass  lifted. 

Gravitational  units  of  force  are  not  strictly  constant 
because  the  weight  of  the  same  mass  varies  from  point  to 
point  on  the  earth's  surface,  and  at  different  elevations. 
The  actual  force  necessary  to  lift  the  mass  of  a  pound  at 
the  poles  of  the  earth  is  greater  than  at  the  equator;  it  is 
less  on  the  top  of  a  high  mountain  than  in  the  neighboring 
valleys,  and  still  less  than  at  the  level  of  the  sea.  Gravi- 
tational units  of  force  are  convenient  for  the  common  pur- 
poses of  life  and  for  the  work  of  the  engineer,  but  they  are 
not  suitable  for  precise  measurements,  especially  in  the 
domain  of  electricity. 

The  so-called  "  absolute  "  unit  of  force  in  the  c.g.s.  system 
is  the  dyne  (from  the  Greek  word  meaning  force).  The 
dyne  is  the  force  which  imparts  to  a  gram  mass  an  acceler- 
ation equal  to  one  centimeter -per-second  per  second.  This 
unit  is  invariable  in  value,  for  it  is  independent  of  the  vari- 
able force  of  gravitation.  It  is  indispensable  in  framing 
the  definitions  of  modern  electrical  and  magnetic  units. 


106  MECHANICS   OF  SOLIDS 

115.  Relation  between  the  Gram  of  Force  and  the  Dyne. — 
The  gram  of  force  is  the  pull  of  the  earth  on  a  mass  of  one 
gram,  definitely  at  sea  level  and  latitude  45°.  Since  the 
attraction  of  the  earth  in  New  York  imparts  to  a  gram 
mass  an  acceleration  of  980  cm.-per-second  per  second, 
while  the  dyne  produces  an  acceleration  of  only  1  cm.-per- 
second  per  second,  it  follows  that  the  gram  of  force  in  New 
York  is  equal  to  980  dynes,  or  the  dyne  is  -g|7  of  the  gram 
of  force.  The  pull  of  gravity  on  a  gram  mass  in  other 
latitudes  is  not  exactly  the  same  as  in  New  York,  but  for 
the  purposes  of  this  book  it  will  be  sufficiently  accurate  to 
say  that  a  gram  of  force  is  equal  to  980  dynes.  It  will  be 
seen,  therefore,  that  the  value  of  any  force  expressed 
in  dynes  is  approximately  980  times  as  great  as  in  grams 
of  force.  Conversely,  to  convert  dynes  into  grams 
of  force,  divide  by  980. 

116.  How  a  Force  is  Measured  Mechanically.  —  The 
simplest  device  for  measuring  a  force  is  the  spring 
balance  (Fig.  104).  The  common  draw  scale  is  a 
spring  balance  graduated  in  pounds  and  fractions 
of  a  pound.  If  a  weight  of  15  lb.,  for  example, 
be  hung  on  the  spring  and  the  position  of  the 
pointer  be  marked,  then  any  other  15  lb.  of  force 
will  stretch  the  spring  to  the  same  extent  in  any 
direction.  If  a  man  by  pulling  in  any  direction 
104.  —  stretches  a  spring  3  in.,  and  if  a  weight  of  150 
SPRING  pounds  also  stretches  the  spring  3  in.,  the  force 

RAT  ATMPP 

"  exerted  by  the  man  is  150  pounds  of  force. 
The  spring  balance  may  be  graduated  in  pounds  of  force, 
kilograms  or  grams  of  force,  or  in  dynes.  If  correctly 
graduated  in  dynes,  it  will  give  right  readings  at  any 
latitude  or  elevation.  Why  are  the  divisions  of  the  scale 
equal? 


COMPOSITION  OF  FORCES  107 

117.  Graphic  Representation  of  a  Force.  —  A   force   has 
not  only  magnitude  but  also  direction;  in  addition,  it  is 
often  necessary  to  know  its  point  of  application.     These 
three  particulars  may  be  represented   by  a  straight  line 
drawn  through  the  point  of  application  of  the  force  in  the 
direction  in  which  the  force  acts,  and  as  many  units  in 
length  as  there  are  units  of  force,  or  some  multiple  or 
submultiple  of  that  number.     If  a  line  1  cm.  long  stands 
for  a  force  of  15  dynes,  a  line 

4  cm.  long,  in  the  direction  -*  ' B 

AB  (Fig.  105),  will  represent  °5' 70^REPRESENT  A 

a   force    of   60  dynes  acting 

in  the  direction  from  A  to  B.     Any  point  on  the  line  AB 

may  be  used  to  indicate  the  point  at  which  the  force  is 

applied. 

If  it  is  desired  to  represent  graphically  the,  fact  that 

two  forces  act  on  a  body  at  the  same  time,  for  example, 

B  4  kg.  of  force  horizontally  and  2  kg. 

tof  force  vertically,  two  lines  are  drawn 
from  the  point  of  application  A  (Fig. 
2 ~* *c   106),  one  2  cm.  long  to  the  right,  and 

FIGURE   106.  —  Two    the  other  1  cm.  long  toward  the  top 
FORCES   AT   RIGHT   of  the  page.     The  lines  AB  and  AC 
represent  the  forces  in  point  of  appli- 
cation, direction,  and  magnitude,  on  a  scale  of  2  kg.  of 
force  to  the  centimeter. 

II.   COMPOSITION  OF  FORCES  AND  OF  VELOCITIES 

118.  Composition  of  Forces.  —  The   resultant  of   two   or 
more  forces  is  a  single  force  which  will  produce  the  same 
effect  on  the  motion  of  a  body  as  the  several  forces  acting 
together.     (Note  the  exception  in  the  case  of  a  couple, 
§  121.)     The  process  of  finding  the  resultant  of  two  or  more 


108 


MECHANICS   OF  SOLIDS 


forces  is  known  as  the  composition  of  forces.  It  will  be  con- 
venient to  consider  first  the  composition  of  parallel  forces, 
and  then  that  of  forces  acting  at  an  angle.  The  several 
forces  are  called  components. 

119.  The  Resultant  of  Parallel  Forces.  —  Suspend  two  draw 
scales,  A  and  B  (Fig.  107),  from  a  suitable  support  by  cords.     Attach 

to  them  a  graduated 
bar  and  adjust  the 
draw  scales  and  the 
attached  cords  so  that 
they  are  vertical. 
Read  the  scales,  then 
attach  the  weight  W 
and  again  read  the 
scales.  Note  the  dis- 
tances CE  and  ED. 
Correct  each  drav: 
scale  reading  by  sub- 
tracting from  it  the 
reading  before  the 
weight  W  was  added. 
Compare  W  with  the 
sum  of  these  corrected 
readings,  and  also  the 
ratio  of  the  corrected 
readings  of  A  and  B 
to  that  of  ED  and  EC. 
Change  the  position  of  E  and  repeat  the  observations.  It  will  be 

A      ~t?  Ty 

found  in  each  case  that  —  = .    Hence  the  following  principle  : 

„  B      EC 

The  resultant  of  two  parallel  forces  in  the  same  direc- 
tion is  equal  to  their  sum;  its  point  of  application 
divides  the  line  joining  the  points  of  application  of  the 
two  forces  into  two  parts  which  are  inversely  as  the 
forces. 

120.  Equilibrium.  —  If  two  or  more  forces  act  on  a  body 
and  no  motion  results,  the  forces  are  said  to  be  in  equi- 


FIGURE  107.  —  PARALLEL  FORCES. 


RESULTANT  OF  TWO  FORCES  AT  AN  ANGLE     109 

librium.  In  Fig.  107  the  weight  W  is  equal  and  opposite 
to  the  resultant  of  the  two  forces  measured  bythe  draw 
scales  A  and  B.  The  three  forces  A,  B,  and  W  are  in 
equilibrium.  Further,  each  force  is  equal  and  opposite  to 
the  resultant  of  the  other  two  and  is  called  their  equi- 
librant.  The  equilibrium  of  a  body  does  not  mean  that 
its  velocity  is  zero,  but  that  its  acceleration  is  zero.  Rest 
means  zero  velocity  ;  equilibrium,  zero  acceleration. 

121.  Parallel  Forces  in  Opposite  Directions.  —  If  two  par- 
allel forces  act  in  opposite  directions,  their  resultant  is 
their  difference,  and  it  acts  in  the  direction  of  the  larger 
force.  In  Fig.  107  the  resultant  of  A  and  W  is  equal  and 
opposite  to  B. 

When  the  two  parallel  forces  acting  in  opposite  direc- 
tions are  equal,  they  form  a  couple.  The  resultant  of  a 
couple  is  zero ;  that  is,  no  single  force  can  be  substituted 
for  it  and  produce  the  same  effect.  A  couple  produces 
motion  of  rotation  only,  in  which  all  the  particles  of  the 
body  to  which  it  is  applied  rotate  in  circles  about  a  com- 
mon axis.  For  example,  a  magnetized  sewing  needle 
floated  on  water  is  acted  on  by  a  couple  when  it  is  dis- 
placed from  a  north-and-south  position.  One  end  of  the 
needle  is  attracted  toward  the  north,  and  the  other  toward 
the  south,  with  equal  and  parallel  forces.  The  effect  is 
to  rotate  the  needle  about  a  vertical  axis  until  it  returns 
to  a  north-and-south  position.  The  common  auger,  as  a 
carpenter  employs  it  to  bore  a  hole,  illustrates  a  couple  in 
the  equal  and  opposite  parallel  forces  applied  by  the  two 
hands. 

122.  The  Resultant  of  Two  Forces  Acting  at  an  Angle.  — 

Tie  together  three  cords  at  D  (Fig.  108)  and  fasten  the  three  ends  to 
the  hooks  of  the  draw  scales  A,  B,  C.  Pass  their  rings  over  pegs  set 
in  a  board  at  such  distances  apart  that  the  draw  scales  will  all  be 


110 


MECHANICS   OF  SOLIDS 


stretched.  Record  the  readings  of  the  scales,  and  by  means  of  a 
protractor  (see  Appendix  I)  measure  the  angles  formed  at  D  by  the 
cords.  Draw  on  a  sheet  of  paper  three  lines  meeting  at  a  point  Z>, 
and  forming  with  one  another  these  angles.  Lay  off  on  the  three 
lines  on  some  convenient  scale,  distances  to  represent  the  readings  of 
the  draw  scales,  DF  for  A,  DE  for  B,  and  DC  for  C.  With  DF  and 
DE  as  adjacent  sides,  complete  the  parallelogram  DFGE  and  draw 
the  diagonal  DG.  DG  is  the  resultant  of  the  forces  A  and  jB,  and  its 


Scale :   50  gm.  to  1  OB. 


\j 

FIGURE  108  —  RESULTANT  OF  Two  FORCES  AT  AN  ANGLE. 

length  on  the  scale  chosen  will  be  found  equal  to  that  of  DC,  their 
equilibrant.  Here  again,  each  force  is  equal  and  opposite  to  the 
resultant  of  the  other  two. 

When  two  forces  act  together  on  a  body  at  an  angle,  the  resultant 
lies  between  the  two  ;  its  position  and  value  may  be  found  by  apply- 
ing the  following  principle,  known  as  the  parallelogram  offerees  : 


If  two  forces  are  represented  by  two  adjacent  sides 
and  DE)  of  a  parallelogram,  their  resultant  is  represented 
by  the  diagonal  (D  6r)  of  the  parallelogram  drawn  through 
their  common  point  of  application 


COMPONENT  IN  A   GIVEN  DIRECTION  111 

When  the  two  forces  are  equal,  their  resultant  lies  mid- 
way between  them.  If  the  two  forces  are  at  right  angles 
(Fig.  109)  the  parallelogram  becomes 
a  rectangle  and  the  two  forces  and 
their  resultant  are  represented  by  the 
three  sides  of  a  right  triangle,  AB, 
ED,  AD.  The  value  of  the  resultant 
in  this  case  may  be  found  by  com-  FIGURE  109.  —  FORCES 
puting  the  hypotenuse  of  the  triangle.  AT  RlGHT  ANGLES> 

For  example,  if  the  forces  at  right  angles  are  6  kg.  of  force  and 
8  kg.  of  force,  their  resultant  is 


V62  +  82  =  10  kg.  of  force. 

123.  Component  of  a  Force  in  a  Given  Direction.  —  It 
frequently  occurs  that  if  a  force  produces  any  motion,  it 

must  be  in  a  direction  other 
than  that  of  the  force  itself. 
For  example,  suppose  the  force 
AB  (Fig.  110)  applied  to  cause 
FIGURE  1 10.  — COMPONENT  IN  a  car  to  move  along  the  rails 

mn.     The  force  AB  evidently 

produces  two  effects ;  it  tends  to  move  the  car  along  the 
rails,  and  it  increases  the  pressure  on  them.  The  two 
effects  are  produced  by  the  two  forces  OB  and  DB  re- 
spectively. They  are  therefore  the  equivalent  of  AB. 
The  force  CB  is  called  the  component  of  AB  in  the  direc- 
tion of  the  rails  mn<  and  DB  is  the  component  perpen- 
dicular to  them.  The  component  of  a  force  in  a  given 
direction  is  its  effective  value  in  this  direction. 

To  find  the  component  in  a  given  direction,  construct  on 
the  line  representing  the  force,  as  the  diagonal,  a  rectangle, 
the  sides  of  which  are  respectively  parallel  and  perpendicular 
to  the  direction  of  the  required  component ;  the  length  of  the 


112 


MECHANICS   OF  SOLIDS 


side  parallel  to  the  given  direction  represents  the  component 
sought. 

EXAMPLE.  Let  a  force  of  200  Ib.  be  applied  to  a  truck,  as  AB  in 
Fig.  110 ;  and  let  it  act  at  an  angle  of  30°  with  the  horizontal.  Find 
the  horizontal  component  pushing  the  truck  forward. 

Construct  a  parallelogram  on  some  convenient  scale  (Appendix  I) 
with  the  angle  ABC  equal  to  30°  and  AB  representing  200  Ib. 
Measure  the  side  CB  and  obtain  by  the  scale  used  its  equivalent  in 
pounds  of  force.  CB  may  be  calculated  since  A  CB  is  a  right  triangle. 
Since  ABC  is  an  angle  of  30°,  AC  is  one  half  of  AB.  Then,  since 
A  C  denotes  100  Ib.  of  force, 


CB  = 


=  V2002  -  1002  =  173.2  Ib.  of  force. 


124.   Illustrations  of  the  Resolution  of  a  Force.  —  The  kite, 
the  sailboat,    and   the  aeroplane   are   familiar   illustrations   of    the 

resolution  of  the  force  of  the  wind. 
In  the  case  of  the  kite,  the  forces 

acting  are  the  weight  of  the  kite  AB 

(Fig.  Ill),  the  pull  of  the  string  A  C, 

and  the  force  of  the  wind  LA.     AD 

is  the  resultant  of  AB  and  A  C.     Re- 

solve the  force  of 

the  wind  into  two 

components,     one 

perpendicular     to 

HK,    the   face   of 

the  kite,  and  the 

other    parallel   to 

HK.  If  HK  sets  itself  at  such  an  angle  that  the 
component  of  LA  perpendicular  to  HK  coincides 
with  AD  and  is  equal  to  it,  the  kite  will  be  in  equi- 
librium ;  if  it  is  greater  than  AD,  the  kite  will  move 
upward  ;  if  less,  it  will  descend. 

In  the  case  of  the  sailboat,  the  sail  is  set  at  such 
an  angle  that  the  wind  strikes  the  rear  face.  In 
Fig.  112  BS  represents  the  sail,  and  AB  the  direc-  FIGURE  112  _ 
tion  and  force  of  the  wind.  This  force  may  be  re-  FORCES  ON  SAIL- 
solved  into  two  rectangular  components,  CB  and  BOAT. 


FIGURE  111.  —  FORCES  ACTING  ON 
KITE. 


COMPOSITION  AND  RESOLUTION  OF  VELOCITIES      113 

DB,  of  which  CB  represents  the  intensity  of  the  force  that  drives  the 
boat  forward. 

In  the  case  of  the  aeroplane  (Fig.  113),  if  a  large  flat  surface, 
placed  obliquely  to  the  ground,  be  moved  along  rapidly,  it  will  be 
lifted  upward  by  the  vertical  component  of  the  reaction  of  the  air 
against  it,  equivalent  to  a  wind,  just  as  the  kite  is  lifted.  In  both  the 
monoplane  and  the  biplane,  large  bent  surfaces  attached  to  a  strong 
light  frame  are  forced  through  the  air  by  a  rapidly  rotating  propeller 
driven  by  a  powerful  gasoline  engine  (§  380).  By  means  of  suitable 


FIGURE  113.  —  THE  FRENCHMAN  VEDRINES  AND  HIS  MONOPLANE. 

levers  under  control  of  the  driver,  these  planes,  or  certain  auxiliary 
planes,  can  be  set  at  an  angle  to  the  stream  of  air  against  which  they 
are  propelled.  Then,  as  with  the  kite,  they  rise  through  the  air. 
Vertical  planes  are  attached  to  the  frame  to  serve  as  rudders  in  steer- 
ing either  to  the  right  or  the  left. 

125.  Composition  and  Resolution  of  Velocities.  —  At  the 
Paris  exposition  in  1900  a  continuous  moving  sidewalk 
carried  visitors  around  the  grounds.  A  person  walking 
on  this  platform  had  a  velocity  with  respect  to  the  ground 
made  up  of  the  velocity  of  the  sidewalk  relative  to  the 
ground  and  the  velocity  of  the  person  relative  to  the  mov- 


114 


MECHANICS   OF  SOLIDS 


ing  walk.  The  several  velocities  entering  the  result  are 
the  component  velocities.  Velocities  may  be  combined  and 
resolved  by  the  same  methods  as  those  applying  to  forces. 
When  several  motions  are  given  to  a  body  at  the  same 
time,  its  actual  motion  is  a  compromise  between  them, 
and  the  compromise  path  is  the  resultant. 

The  following  is  an  example  of  the  composition  of  two  velocities 
at  right  angles :  A  boat  can  be  rowed  in  still  water  at  the  rate  of  5 
mi.  an  hour ;  what  will  be  its  actual  velocity  if  it  be  rowed  5  mi.  an 
hour  across  a  stream  running  3  mi.  an  hour  ? 

Let  AB  (Fig.  114)  represent  in  length  and  direction  the  velocity  of 
5  mi.  an  hour  across  the  stream,  and  AC,  at  right  angles  to  AB,  the 
velocity  of  the  current,  3  mi.  an  hour,  both 
on  the  same  scale.     Complete  the  parallelo- 
gram ABDC,  and  draw  the  diagonal  AD 
through  the  point  A   common  to  the  two 
component   velocities.     AD  represents    the 
actual  velocity  of  the  boat ;  its  length  on  the 
same  scale  as  that  of  the  other  lines  is  5.83. 
The  resultant  velocity  is  therefore  5.83  miles 
an  hour  in  the  direction  AD. 
When  the  angle  between  the  components  is  a  right  angle,  as  in  the 
present  case,  the  diagonal  AD  is  the  hypotenuse  of  the  right  triangle 
ABD.    Its  square  is  therefore  the  sum  of  the  squares  of  5  and  3,  or 

AD  =  V52  +  32  =  5.83. 

When  the  angle  at  A  is  not  a  right  angle,  the  approximate  resultant 
may  be  found  by  a  graphic  process  of  measurement. 

A  velocity,  like  a  force,  has  both  direction  and  magni- 
tude, and  a  component  of  it  in  any  given  direction  may  be 
found  in  precisely  the  same  way  as  in  the  case  of  a  force, 
(§  123).  The  most  common  case  is  the  resolution  into 
components  at  right  angles  to  each  other.  In  most  cases 
it  suffices  to  find  the  component  in  the  direction  in  which 
the  attention  for  the  time  being  is  directed.  The  other  one 
at  right  angles  is  without  effect  in  this  particular  direction. 


FIGURE  1 14. — BOAT  RUN- 
NING ACROSS  STREAM. 


PROBLEMS  115 


Problems 

NOTE.  —  Solve  graphically  the  problems  involving  forces  and  velocities  at 
an  angle.  Where  possible,  verify  by  calculation.  Consult  Appendix  I  for 
methods  of  drawing. 

1.  Plot  a  force  of  25  g.  on  a  scale  of  4  cm.  to  the  gram. 

2.  Represent  a  force  of  50  g.  by  a  straight  line  on  a  scale  of 
10  cm.  to  the  gram. 

3.  Represent  by  a  figure  two  forces  acting  at  a  common  point, 
the  forces  being  15  g.  and  20  g.  respectively,  and  the  angle  between 
their  directions  being  60°. 

4.  A  body  is  acted  on  by  two  parallel  forces,  20  and  30  Ib.  respec- 
tively.    These  forces  act  in  the  same  direction  and  have  their  points 
of  application  60  in.  apart.     Find  the  magnitude  of  the  resultant  and 
the  distance  of  its  point  of  application  from  the  less  force. 

SUGGESTION.  —  Let  x  be  the  distance  of  the  point  of  application  of  the 
resultant  from  the  force  20.  Then  60  —  x  will  be  the  distance  from  the 

force  30.    Then  by  Art.  119,  ^  =  ^=^  . 


5.  A  weight  of  200  Ib.  is  fastened  to  the  middle  of  a  bar  four  feet 
long.     A  boy  and  a  man  take  hold  of  the  bar  to  carry  it.     The  boy 
takes  hold  at  one  end  of  the  bar.     Find  where  the  man  must  take 
hold  so  that  he  will  carry  two-thirds  of  the  load. 

6.  A  horse  and  a  colt  are  hitched  side  by  side  in  the  usual  manner 
to  a  loaded  wagon.    A  force  of  300  Ib.  will  just  move  the  wagon.     At 
what  point  of  the  double-tree  must  it  be  attached  to  the  tongue  of 
the  wagon  so  that  the  colt  will  pull  two  pounds  to  the  horse's  three, 
the  double-tree  being  40  in.  long. 

7.  A  stiff  bar  firmly  fastened  at  one  end  sticks  out  horizontally 
over  a  cliff  for  10  ft.,  and  will  just  support  without  breaking  a  weight 
of  100  Ib.  at  the  outer  end.     How  far  out  on  the  bar  may  a  weight  of 
150  Ib.  be  placed  with  safety? 

8.  Resolve  a  force  of  50  dynes  into  two  parallel  forces,  with  their 
points  of  application  20  and  30  cm.  respectively  from  the  given  force. 

9.  Two  forces,  30  and  40  grams,  act  on  a  body  at  an  angle  of  60°. 
Find  the  resultant. 

10.    A  ball  is  given  an  eastward  direction  by  the  action  of  a  force 
of  20  dynes.     At  the  same  time  a  force  of  30  dynes  acts  on  the  ball 


116  MECHANICS  OF  SOLIDS 

to  give  it  a  northward  direction.     In  what  direction  does  it  go,  and 
what  single  force  will  produce  the  same  effect  ? 

11.  In  towing  a  boat  along  a  stream  two  ropes  were  used,  the  angle 
between  them  when  taut  being  45°.     A  force  of  100  Ib.  was  acting  on 
one  rope  and  150  Ib.  on  the  other.    What  resistance  did  the  boat  offer 
to  being  moved  ? 

12.  A  sailboat  is  going  eastward,  the  wind  is  from  the  northwest, 
and  the  sail  is  set  at  an  angle  of  30°  with  the.  direction  of  the  wind. 
If  the  wind's  velocity  is  12  miles  an  hour,  what  is  the  component 
velocity  at  right  angles  to  the  sail  ? 

III.   NEWTON'S  LAWS  OF  MOTION 

126.  Momentum.  —  So  far  we  have  considered  different 
kinds  of  motion,  or  how  bodies  move,  without  reference  to 
the  mass  moved,  and  without   considering   the   relation 
between  force  on  the  one  hand  and  the  moving  mass  and 
its  velocity  on  the  other,  or  why  bodies  move.     Before 
taking  up  the  laws  of  motion,  which  outline  the  relations 
between  force  and  motion,  it  is  necessary  to  define  two 
terms  intimately  associated  with  these  laws.     The  first  of 
these  is  momentum.     Momentum  is  the  product  of  the  mass 
and  the  linear  velocity  of  a  moving  body. 

Momentum  —  mass  x  velocity,  or  M  =  mv.     (Equation  8) 

In  the  c.g.s.  system,  the  unit  of  momentum  is  the  mo- 
mentum of  a  mass  of  1  g.  moving  with  a  velocity  of  1  cm. 
per  second.  It  has  no  recognized  name.  In  the  English 
system,  the  unit  of  momentum  is  the  momentum  of  a  mass 
of  1  Ib.  moving  with  a  velocity  of  1  ft.  per  second. 

127.  Impulse.  —  Suppose  a  ball  of  10  g.  mass  to  be  fired 
from  a  rifle  with  a  velocity  of  50,000  cm.  per  second.     Its 
momentum  would  be  500,000  units.     If  a  truck  weighing 
50  kg.  moves  at  the  rate  of  10  cm.  per  secpnd,  its  momen- 
tum is  also  500,000  units.     But  the  ball  has  acquired  its 


FIRST  LAW  OF  MOTION  117 

momentum  in  a  fraction  of  a  second,  while  a  minute  or 
more  may  have  been  spent  in  giving  to  the  truck  the 
same  momentum.  In  some  sense  the  effort  required  to 
set  the  ball  in  motion  is  the  same  as  that  required  to 
give  the  equivalent  amount  of  motion  to  the  truck,  be- 
cause the  momenta  of  the  two  are  equal. 

This  equality  is  expressed  by  saying  that  the  impulse  is 
the  same  in  the  two  cases.  Since  the  effect  is  doubled 
if  the  value  of  the  force  is  doubled,  or  if  the  time  during 
which  the  force  continues  to  act  is  doubled,  it  follows  that 
impulse  is  the  product  of  the  force  and  the  time  it  continues 
to  act.  In  estimating  the  effect  of  a  force,  the  time  ele- 
ment and  the  magnitude  of  the  force  are  equally  impor- 
tant. The  term  impulse  takes  both  into  account. 

128.  Newton's  Laws  of  Motion.  —  The  laws  of   motion, 
formulated  by  Sir  Isaac  Newton  (1642-1727),  are  to  be 
regarded  as  physical  axioms,  incapable  of  rigorous  experi- 
mental proof.     They  must  be  considered  as  resting  on 
convictions  drawn  from    observation   and  experiment  in 
the  domain  of  physics  and  astronomy.     The  results  de- 
rived from  their  application  have  so  far  been  found  to  be 
invariably  true.     They  form  the  basis  of  many  of  the 
important  principles  of  mechanics. 

129.  First  Law  of  Motion.  —  Every  body  continues  in 
its  state  of  rest  or  of  uniform  motion  in  a  straight  line, 
unless  compelled  by  applied  force  to  change  that  state. 

This  is  known  as  the  law  of  inertia  (§  9),  because  it 
asserts  that  a  body  persists  in  a  condition  of  rest  or  of 
uniform  motion,  unless  it  is  compelled  to  change  that 
state  by  the  action  of  an  external  force.  It  is  further 
true  that  a  body  offers  resistance  to  any  such  change  in 


118  MECHANICS  OF  SOLIDS 

proportion  to  its  mass.     Hence  the  term  mass  is  now  often 
used  to  denote  the  measure  of  a  body's  inertia  (§  11). 

From  this  law  is  also  derived  the  Newtonian  definition 
of  force,  for  the  law  asserts  that  force  is  the  sole  cause  of 
change  of  motion. 

130.  Second  Law  of  Motion.  —  Change  of  momentum  is 
proportional  to  the  impressed  force  which  produces  it, 
and  takes  place  in  the  direction  in  which  the  force  acts. 

The  second  law  points  out  two  things : 

First.  What  the  measure  is  of  a.  force  which  produces 
change  of  motion.  Maxwell  restated  the  second  law  in 
modern  terms  as  follows  :  "  The  change  of  momentum  of  a 
body  is  numerically  equal  to  the  impulse  which  produces  it, 
and  is  in  the  same  direction  "  ;  or  in  other  words, 

momentum  (mass  x  velocity)  =  impulse  (force  x  time). 
Expressed  in  symbols,      mv=ft.      .     .     .     (Equation  9) 

TT  /.     mv 

Hence,  /  =  — . 

t 

The  initial  velocity  of  the  mass  m  before  the  force  / 
acted  on  it  is  here  assumed  to  be  zero,  and  v  is  the  veloc- 
ity attained  in  t  seconds.  Then  the  total  momentum  im- 
parted in  the  time  t  is  mv,  and  therefore  -  -  is  the  rate  of 

t 

change  of  momentum.     Force  is  therefore  measured  by  the 

rate  of  change  of  momentum.     Since  -  is  the  rate  of  change 

t 

of  velocity,  or  the  acceleration  a  (see  Equation  5),  we  may 

write 

/=  ma.     .     .     .     (Equation  10) 


THIRD  LAW  OF  MOTION  119 

We  see  from  this  that  force  may  also  be  measured  by  the 
product  of  the  mass  moved  and  the  acceleration  imparted  to 
it.  Therefore  when  the  mass  m  is  unity,  the  force  is 
numerically  equal  to  the  acceleration  it  produces.  Hence 
the  definition  of  the*  dyne  (§  114). 

Second.  This  law  also  points  out  that  the  change  of 
momentum  is  always  in  the  direction  in  which  the  force  acts. 
Hence,  when  two  or  more  forces  act  together,  each  pro- 
duces its  change  of  momentum  independently  of  the  others 
and  in  its  own  direction.  This  principle  lies  at  the  founda- 
tion of  the  method  of  finding  the  resultant  effect  of  two 
forces  acting  on  a  body  in  different  directions  (§  118). 

On  a  horizontal  shelf  about  two  meters  above  the  floor  are  placed 
two  marbles,  one  on  each  side  of  a  straight  spring  fixed  vertically  over 
a  hole  in  the  shelf.     One  marble  rests 
on  the  shelf  and  the  other  is  held  over 
the  hole    between    the    spring    and    a 
block  fixed  to  the  shelf  (Fig.  115).     When 
the  hammer  falls  and  strikes  the  spring,  it  pro- 
jects the  one  marble  horizontally  and  lets  the  other 
one  fall  vertically.     The  two  reach  the  floor  at  the 
same  instant.     Both  marbles  have  the  same  vertical 
acceleration.  FIGURE   1 15. 

—  ILLUSTRATING 

131 .   Third  Law  of  Motion. — To  every  action  SECOND  LAW  OF 
there  is  always  an  equal  and  contrary  re- 
action ,*  or  the  mutual  actions  of  two  bodies  are  always 
equal  and   oppositely  directed. 

The  essence  of  this  law  is  that  all  action  between  two 
bodies  is  mutual.  Such  action  is  known  as  a  stress  and  a 
stress  is  always  a  two-sided  phenomenon,  including  both 
action  and  reaction.  The  third  law  teaches  that  these  two 
aspects  of  a  stress  are  always  equal  and  in  opposite  direc- 
tions. The  stress  in  a  stretched  elastic  cord  pulls  the  two 


120 


MECHANICS  OF  SOLIDS 


bodies  to  which  it  is  attached  equally  in  opposite  directions; 
the  stress  in  a  compressed  rubber  buffer  or  spring  exerts 
an  equal  push  both  ways ;  the  former  is  called  a  tension 
and  the  latter  a  pressure. 

. '<\  *•-"•••  • 
ILLUSTRATIONS.     The  tension  in  a  rope  supporting  a  weight  is  a 

stress  tending  to  part  it  by  pulling  adjacent  portions  in  opposite 
directions.  The  same  is  obviously  true  if  two  men  pull  at  the  ends  of 


AMERICAN  AIRPLANE  SQUADRON  IN  FORMATION. 
Note  the  perfect  alinement. 


the  rope.  An  ocean  steamship  is  pushed  along  by  the  reaction  of  the 
water  against  the  blades  of  the  propeller.  The  same  is  true  of  an 
aeroplane,  only  in  this  case  the  reaction  against  the  blades  is  by  the 
air,  and  the  blades  are  longer  and  revolve  much  faster  than  in  water 
in  order  to  move  enough  air  to  furnish  the  necessary  reaction.  When 
a  man  jumps  from  a  rowboat  to  the  shore,  he  thrusts  the  boat  back- 
wards. An  athlete  would  not  make  a  record  standing  jump  from  a 
feather  bed  or  a  spring  board.  When  a  ball  is  shot  from  a  gun,  the 
gun  recoils  or  "  kicks."  All  attraction,  such  as  that  between  a  mag- 
net and  a  piece  of  iron,  is  a  stress,  the  magnet  attracting  the  iron  and 
the  iron  the  magnet  with  the  same  force. 


PROBLEMS 


121 


Practical  use  is  made  of  reaction  to  turn  the  oscillating  electric  fan 
from  side  to  side  so  as  to  blow  the  air  in  different  directions.  A  rec- 
tangular sheet  of  brass  is  bent  lengthwise  at  right  angles  and  is  pivoted 
so  as  to  turn  90°  about  a  vertical  axis  (Fig. 
116).  When  one  half  of  this  bent  sheet  is  ex- 
posed to  the  air  current,  the  reaction  sustained 
by  the  blades  of  the  fan  on  this  side  is  in  part 
balanced  by  the  reaction  of  the  bent  sheet; 
but  on  the  opposite  half  of  the  fan  the  reaction 
of  the  blades  is  not  balanced.  Hence  the 
whole  fan  turns  about  a  vertical  axis  on  the- 
standard  until  a  lever  touches  a  stop  and  shifts 
the  bent  strip  so  as  to  expose  the  other  half 
of  it  to  the  air  current  from  the  opposite  half 
of  the  fan.  The  fan  then  reverses  its  slow 
motion  and  turns  to  the  other  side. 


FIGURE     116.  —  OSCIL- 
LATING FAN. 


Since  force  is  measured  by  the  rate  at  which  momentum 
changes,  the  third  law  of  motion  is  equivalent  to  the  fol- 
lowing: 

In  every  action  between  two  bodies,  the  momentum 
gained  by  the  one  is  equal  to  that  lost  by  the  other,  or  the 
momenta  in  opposite  directions  are  the  same. 


Problems 

1.  What    relative  velocities  will   equal  impulses  impart  to  the 
masses  5  Ib.  and  8  Ib.  respectively  ? 

2.  A  body  of  50  g.  is  moving  with  a  velocity  of  20  cm.  per  second. 
What  is  its  momentum  ? 

3.  Find  the  ratio  of  the   momentum   of  a  body  whose  mass  is 
10  Ib.,  moving  with  a  uniform  velocity  of  50  ft.  per  second  to  that  of  a 
body  whose  mass  is  25  Ib.  and  whose  velocity  is  20  ft.  per  second. 

4.  Two  bodies  have  equal  momenta.     One  has  a  mass  of  2  Ib.  and 
a  velocity  of  1500  ft.  per  second,  the  other  a  mass  of  100  Ib.     What  is 
the  velocity  of  the  second  body  ? 

5.  What  is  the  velocity  of  recoil  of  a  gun  whose  mass  is  5  kg.,  the 
mass  of  the  ball  being  25  g.  and  its  velocity  600  m.  per  second? 


122  MECHANICS  OF  SOLIDS 

6.  An  unbalanced  force  of  500  dynes  acts  for  5  sec.  on  a  mass  of 
50  g.    "What  will  be  the  velocity  produced  ? 

7.  A  force  of  980  dynes  acts  on  a  mass  of  1  g.     What  is  the 
acceleration  ?     How  far  will  the  body  go  in  10  sec.  ? 

8.  A  force  of  400  dynes  acts  on  a  body  for  10  sec.     What  will  be 
the  momentum  at  the  end  of  this  period? 

9.  A  body  is  acted  on  by  a  force  of  100  dynes  for  20  sec.  and 
acquires  a  velocity  of  200  cm.  per  second.     What  is  its  mass? 

10.  A  force  of  10  g.  acts  for  5  sec.  on  a  body  whose  mass  is  15  g. 
What  velocity  is  imparted  ? 

11.  What  force  in  grams  of  force  can  impart  to  a  mass  of  50  g.  an 
acceleration  of  980  cm.-per-second  per  second? 

12.  A  force  of  50  g.  acts  for  5  sec.  on  a  mass  of  50  g.     How  far 
will  the  body  have  gone  in  that  time,  starting  from  rest  ? 

IV.   GRAVITATION 

132.  Weight. —  The  attraction  of  the  earth  for  all  bodies  is 
called  gravity.     The  weight  of  a  body  is  the  measure  of  this 
attraction.     It  is  a  pull  on  the  body  and  therefore  a  force. 
It  makes  a  body  fall  with  uniform  acceleration  called  the 
acceleration  of  gravity  and  denoted  by  g.     If  we  represent 
the  weight  of  a  body  by  w  and  its  mass  by  w,  by  Equation 
10,  w  =  mg.     From  this  it  appears  that  the  weight  of  a  body 
is  proportional  to  its  mass,  and  that  the  ratio  of  the  weights 
of  two  bodies  at  anyplace  is  the  same  as  that  of  their  masses. 
Hence,  in  the  process  of  weighing  with  a  beam  balance, 
the  mass  of  the  body  weighed  is  compared  with  that  of  a 
standard  mass.     When  a  beam  balance  shows  equality  of 
weights,  it  shows  also  equality  of  masses. 

133.  Direction  of  Gravity.  —  The  direction  in  which  the 
force  of  gravity  acts  at  any  point  is  very  nearly  toward 
the  earth's  center.     It  may  be  determined  by  suspending 
a  weight  by  a  cord  passing  through  the  point.     The  cord 


LAW  OF  UNIVERSAL   GRAVITATION  123 

is  called  a  plumb  line  (Fig.  117),  and  its  direction  is  a  ver- 
tical line.  A  plane  or  line  perpendicular  to  a  plumb  line 
is  said  to  be  horizontal.  Vertical  lines  drawn 
through  neighboring  points  may  be  considered 
parallel  without  sensible  error. 

134.  Center  of  Gravity.  —  In   Physics  a  body  is 
thought  of  as  composed  of  an  indefinitely  large 
number  of  parts,  each  of  which  is  acted  on  by 
gravity.     For  bodies  of  ordinary  size,  these  forces 
of  gravity  are  parallel  and  proportional  to  the 
masses  of  the  several  small  parts.      The  point  of 
application  of  their  resultant  is  the  center  of  gravity 
of  the  body. 

If  the  body  is  uniform  throughout,  the  position 
of  its  center  of  gravity  depends  on  its  geometri- 
cal figure  only.  Thus,  the  center  of  gravity  (1) 
of  a  straight  rod  is  its  middle  point ;  (2)  of  a 
circle  or  ring,  its  center  ;  (3)  of  a  sphere  or  a 
spherical  shell,  its  center  ;  (4)  of  a  parallelo- 
gram, the  intersection  uf  its  diagonals  ;  (5)  of  a 
cylinder  or  a  cylindrical  pipe,  the  middle  point  of 
its  axis.  i  i  7  e 

It  is  necessary  to  guard  against  the  idea  that  P  L  u  M  F 
the  force  of  gravity  on  a  body  acts  at  its  center  of  INE' 
gravity.  Gravity  acts  on  all  the  particles  composing  the 
body,  but  its  effect  is  generally  the  same  as  if  the  resultant, 
that  is,  the  weight  of  the  body,  acted  at  its  center  of  gravity. 
It  will  be  seen  from  the  examples  of  the  ring  and  the  cylin- 
drical pipe  that  the  center  of  gravity  may  lie  entirely  out- 
side the  body. 

135.  Law  of  Universal  Gravitation.  —  It  had  occurred  to 
Galileo  and  the  other  early  philosophers  that  the  attrac- 
tion of  gravity  extends  beyond  the  earth's  surface,  but  it 


124  MECHANICS  OF  SOLIDS 

remained  for  Sir  Isaac  Newton  to  discover  the  law  of  uni- 
versal gravitation.  He  derived  this  great  generalization 
from  a  study  of  the  planetary  motions  discovered  by  Kep* 
ler.  .The  law  may  be  expressed  as  follows  : 

Every  portion  of  matter  in  the  universe  attracts  every 
other  portion,  and  the  stress  between  them  is  directly  pro- 
portional to  the  product  of  their  masses  and  inversely 
proportional  to  the  square  of  the  distance  between  their 
centers  of  mass. 

For  spherical  bodies,  like  the  sun,  the  earth,  and  the 
planets,  the  attraction  of  gravitation  is  the  same  as  if  all 
the  matter  in  them  were  concentrated  at  their  centers; 
hence,  in  applying  to  them  the  law  of  gravitation,  the 
distance  between  them  is  the  distance  between  their  cen- 
ters. Calculations  made  to  find  the  centripetal  accelera- 
tion of  the  moon  in  its  orbit  show  that  it  is  attracted  to 
the  earth  with  a  force  which  follows  the  law  of  universal 
gravitation. 

The  law  of  universal  gravitation  does  not  refer  in  any  way  to 
weight  but  to  mass.  It  would  be  entirely  meaningless  to  speak  of  the 
weight  of  the  earth,  or  of  the  moon,  or  of  the  sun,  but  their  masses  are 
very  definite  quantities,  the  ratios  of  which  are  well  known  in  as- 
tronomy. Thus  the  mass  of  the  earth  is  about  80  times  that  of 
the  moon,  and  the  mass  of  the  sun  is  about  332,000  times  that  of  the 
earth.  The  weight  of  a  pound  mass  at  the  distance  of  the  moon  is 
only  jgVrr  the  weight  of  a  pound  mass  at  the  surface  of  the  earth. 


136.  Variation  of  Weight.  —  Since  the  earth  is  not  a 
sphere  but  is  flattened  at  the  poles,  it  follows  from  the 
law  of  gravitation  that  the  acceleration  of  gravity,  and 
the  weight  of  any  body,  increase  in  going  from  the  equa- 
tor toward  either  pole.  If  the  earth  were  a  uniform 
sphere  and  stationary,  the  value  of  g  would  be  the  same 


Sir  Isaac  Newton  (1642-1727)  is  celebrated  for  his  discoveries 
in  mathematics  and  physics.  He  was  a  Fellow  of  Trinity  Col- 
lege, Cambridge.  He  discovered  the  binomial  theorem  in  alge- 
bra and  laid  the  foundation  of  the  calculus.  His  greatest  work  is 
the  Principia,  a  treatise  on  motion  and  the  laws  governing  it.  His 
greatest  discoveries  are  the  laws  of  gravitation  and  the  composi- 
tion of  white  light. 

From  Kepler's  laws  of  the  planetary  orbits  Newton  proved  that 
the  attraction  of  the  sun  on  the  planets  varies  inversely  as  the 
squares  of  their  distances. 

He  was  also  distinguished  in  public  life.  He  sat  in  Parliament 
for  the  University  of  Cambridge,  was  at  one  time  Master  of  the 
Mint,  and  the  reformation  of  the  English  coinage  was  largely  his 
work. 


EQUILIBRIUM   UNDER   GRAVITY  125 

all  over  its  surface.  But  the  value  of  g  varies  from  point 
to  point  on  the  earth's  surface,  even  at  sea  level,  both 
because  the  earth  is  not  a  sphere  and  because  it  rotates 
on  its  axis.  The  centripetal  acceleration  of  a  point  at 
the  equator,  owing  to  the  earth's  rotation  on  its  axis,  is 
^Q  the  acceleration  of  gravity  g.  Since  289  is  the 
square  of  17,  and  the  centripetal  acceleration  varies  as 
the  square  of  the  velocity  (§  110),  it  follows  that  if  the 
earth  were  to  rotate  in  one  seventeenth  of  a  day,  that  is, 
'  17  times  as  fast  as  it  now  rotates,  the  apparent  value  of 
g  at  the  equator  would  become  zero,  and  bodies  there 
would  lose  all  their  weight. 

The  value  of  g  at  the  equator  is  978.1  and  at  the  poles 
983.1,  both  in  centimeters-per-second  per  second.  At 
New  York  it  is  980.15  centimeters-per-second  per  second, 
or  32.16  feet-per-second  per  second. 

137.  Equilibrium  under  Gravity.  —  When  a  body  rests  on 
a  horizontal  plane,  its  weight  is  equal  and  opposite  to  the 
reaction  of  the  plane.  The  vertical  line  through  its  cen- 
ter of  gravity  must  therefore  fall  within  its  base  of  sup- 
port. If  this  vertical  line  falls  outside  the  base,  the 
weight  of  the  body  and  the  reaction  of  the  plane  form  a 
couple  (§  121),  and  the  body  overturns. 

The  three  kinds  of  equilibrium  are  >(!)  stable,  for  any 
displacement  which  causes  the  center  of  gravity  to  rise ; 
(2)  unstable,  for  any  displacement  which  causes  the  cen- 
ter of  gravity  to  fall ;  (3)  neutral,  for  any  displacement 
which  does  not  change  the  height  of  the  center  of  gravity. 

Fill  a  round-bottomed  Florence  flask  one  quarter  full  of  shot  and 
cover  them  with  melted  paraffin  to  keep  them  in  place  (Fig.  118). 
Tip  the  flask  over ;  after  a  few  oscillations  it  will  return  to  an  up- 
right position.  Repeat  the  experiment  with  a  similar  empty  flask; 
it  will  not  stand  up,  but  will  rest  in  any  position  on  its  side  and  with 


126 


MECHANICS   OF  SOLIDS 


the  top  on  the  table.     The  loaded  flask  cannot  be  tilted  over  without 
raising  its   center  of  gravity;  in  a  vertical  position   it  is  therefore 

stable  and  when  tipped  over, 
unstable,  for  it  returns  to 
a  vertical  position.  For  the 
empty  flask,  its  center  of  grav- 
ity is  lower  when  it  lies  on  its 
side  than  when  it  is  erect. 
Rolling  it  around  does  not 
change  the  height  of  its  center 

FIGURE  1 18.  -  STABILITY  OF  FLASKS.       of  Sravity  and  its  equilibrium 

is  thus  neutral. 

The  three  funnels  of  Fig.  119  illustrate  the  three  kinds  of  equi- 
librium on  a  plane. 

A  rocking  horse,  a  rocking 
chair,  and  a  half  sphere  resting 
on  its  convex  side  are  examples 
of  stable  equilibrium.  An  egg 
lying  on  its  side  is  in  neutral 
equilibrium  for  rolling  and 
stable  equilibrium  for  rocking ; 
it  is  unstable  on  either  end. 
A  lead  pencil  supported  on  its 
point  is  in  unstable  equilib- 

Any  such  body  may  become  stable  by  attaching  weights  to 
it  in  such  a  manner  as  to  lower  the  center  of 
gravity  below  the  supporting  point  (Fig.  120). 

138.  Stability.  —  Stability  is  the  state  of 
being  firm  or  stable.  The  higher  the  center 
of  gravity  of  a  body  must  be  lifted  to  put 
the  body  in  unstable  equilibrium  or  to 
overturn  it,  the  greater  is  its  stability. 
This  condition  is  met  by  a  relatively  large 
base  and  a  low  center  of  gravity.  A 
pyramid  is  a  very  stable  form.  On  account  of  the  large 
area  lying  within  the  four  feet  of  a  quadruped,  its  stability 
is  greater  than  that  of  a  biped.  A  child  is  therefore  able 


FIGURE  119.  —  STABILITY  OF  FUNNELS. 


num. 


FIGURE  120.— 
CENTER  OF  GRAVITY 
BELOW  SUPPORT. 


QUESTIONS  AND  PROBLEMS 


127 


to  creep  "  on  all  fours  "  before  it  learns  to  maintain  stable 
equilibrium  in  walking.  A  boy  on  stilts  has  smaller  sta- 
bility than  on  his  feet  because  his  support  is  smaller  and 
his  center  of  gravity  higher. 

Stability  may  be  well  illustrated  by  means  of   a  brick.     It  has 
greater  stability  when  lying  on  its  -narrow  side  (2"  x  8")  than  when 
standing  on  end;    and  on  its 
broad  side  (4"  x  8")   its  sta-  ^-^ 

bility  is  still  greater.     Let  Fig.         /'      \ 

A    \ 
\^-\d 


121  represent  a  brick  lying  on 
its  narrow  side  in  A  and  stand- 
ing on  end  in  B.     In  both  case", 
to  overturn   it   its  center  of 
gravity  c  is  lifted  to  the  same    FIGURE    121.  —  DEGREES   OF  STABILITY. 
height,  but  the  vertical  dis- 
tance bd  through  which  the  center  of  gravity  must  be  lifted  is  greater 
in  A  than  in  B. 

A  tall  chimney  or  tower  has  no  great  stability  because  its  base  is 
relatively  small  and  its  center  of  gravity  high.  A  high  brick  wall 
is  able  to  support  a  great  crushing  weight,  but  its  stability  is  small 
unless  it  is  held  by  lateral  walls  and  floor  beams. 

Questions  and  Problems 

1.  If  one  jumps  off  the  top  of  an  empty  barrel  standing  on  end, 
why  is  one  likely  to  get  a  fall? 

2.  Where  is  the  center  of  gravity  of 
a  knife  supported  as  in  Fig.  122  ? 

3.  Given  a  triangle  cut  from  a  uni- 
form sheet  of  cardboard  or  thin  wood. 
Describe  two   methods  of    finding  its 
center  of   gravity.     How  can  you  tell 
when  the  right  center  has  been  found  ? 

4.  Represent  a  hill  by  the  hypotenuse 
of  a  right  triangle,  and  a  ball  on  the  hill 

by  a  circle,  the  circumference  of  the  circle  just  touching  the  hypote- 
nuse of  the  triangle.  How  would  you  represent  the  weight  of  the  ball  ? 
By  resolving  this  force  into  two  components,  find  the  force  that  rolls 


FIGURE  122. 


128 


MECHANICS  OF  SOLIDS 


the  ball  down  the  hill   and  the  force  with  which  the  ball  presses 
against  it. 

5.  Which  is  less  likely  to  "  turn  turtle  "  in  rounding  a  sharp  curve, 
an  underslung  or  an  overslung  automobile  ?    Why? 

6.  A  body  weighing  150  Ib.   on  a  spring  balance  on  the  earth 
would  weigh  how  much  on  the  moon,  the  radius  of  the  moon  being 

that  of  the  earth  and  its  mass      ? 


FIGURE  123.  —  CATHEDRAL  OF  PISA  AND  LEANING  TOWER. 

7.  If  the  acceleration  of  gravity  is  32.2  ft.-per-second  per  second 
on  the  earth,  what  must  it  be  on  the  sun,  the  radius  of  the  sun  being 
taken  as  110  times  that  of  the  earth  and  its  mass  as  330,000  times  ? 

8.  With  what  force  will  a  man  weighing  160  Ib.  press  on  the  floor 
of  an  elevator  when  it  starts  with  an  acceleration  of  4  ft.-per-second 
per  second,  — first  going  up,  and  then  going  down? 

V.   FALLING  BODIES 

139,  Bate  at  which  Different  Bodies  Fall.  —  It  is  a  familiar 
fact  that  heavy  bodies,  such  as  a  stone  or  a  piece  of  iron, 


RESISTANCE  OF  THE  AIR 


129 


fall  much  faster  than  such  light  bodies  as  feathers,  bits  of 
paper,  and  snow  crystals.  Before  the  time  of  Galileo  it 
was  supposed  that  different  bodies  fall  with  velocities  pro- 
portional to  their  weights.  This  erroneous  notion  was 
corrected  by  Galileo  by  means  of  his  famous  experiment 
of  dropping  various  bodies  from  the  top  of  the  leaning 
tower  of  Pisa  (Fig.  123)  in  the  presence  of  professors  and 
students  of  the  university  in  that  city.  He  showed  that 
bodies  of  different  materials  fell  from  the  top  of  the  tower 
to  the  ground,  a  height  of  180  feet,  in  practically  the  same 
time;  also  that  light  bodies,  such  as  paper,  fell  with  ve- 
locities approaching  more  and  more  nearly  those  of  heavy 
bodies  the  more  compactly  they  were  rolled  together  in  a 
ball.  The  slight  differences  in  the  velocities  observed  he 
rightly  ascribed  to  the  resistance  of  the  air, 
which  is  relatively  greater  for  light  bodies 
than  for  heavy  compact  ones.  This  inference 
Galileo  could  not  completely  verify  because 
the  air  pump  had  not  yet  been  invented. 

140.  Resistance  of  the  Air.  —  Place  a  small  coin 
and  a  feather,  or  a  shot  and  a  bit  of  tissue  paper,  in 
a  glass  tube  from  4  to  6  feet  long.  It  is  closed  at  one 
end  and  fitted  with  a  stopcock  at  the  other  (Fig.  124). 
Hold  the  tube  in  a  vertical  position  and  suddenly  in- 
vert it ;  the  coin  or  the  shot  will  fall  to  the  bottom 
first.  Now  exhaust  the  air  as  perfectly  as  possible ; 
again  invert  the  tube  quickly ;  the  lighter  body  will 
now  fall  as  fast  as  the  heavier  one.  This  experiment  is 
known  as  the  "  Guinea  and  Feather  Tube."  It  demon- 
strates that  if  the  resistance  of  the  air  were  wholly  re- 
moved, all  bodies  at  the  same  place  would  fall  with 
eration. 

An  interesting  modification  of  the  experiment  is 
Cut  a  round  piece  of  paper  slightly  smaller  than  a 
the  cent  and  the  paper  side  by  side;  the  cent  will 


FIGURE  124. 
—  GUINEA  AND 
FEATHER  TUBE. 

the  same  accel- 


the  following: 
cent  and  drop 
reach  the  floor 


130  MECHANICS   OF  SOLIDS 

first.  Then  lay  the  paper  on  the  cent  and  drop  them  in  that  position ; 
the  paper  will  now  fall  as  fast  as  the  cent.  Explain. 

The  friction  of  the  air  against  the  surface  of  bodies  moving  through 
it  limits  their  velocity.  A  cloud  floats,  not  because  it  is  lighter  than 
the  atmosphere,  for  it  is  actually  heavier,  but  because  the  surface  fric- 
tion is  so  large  in  comparison  with  the  weight  of  the  minute  drops  of 
water,  that  the  limiting  velocity  of  fall  is  very  small. 

When  a  stream  of  water  flows  over  a  high  precipice,  it  is  broken 
into  fine  spray  and  falls  slowly.  At  the  Yosemite  Fall  (Fig.  125)  a 
large  stream  is  broken  by  the  resistance  of  the  air  until  at  the  bottom 
of  its  1400  foot  drop  it  becomes  fine  spray. 

141.  Laws  of  Falling  Bodies.  —  Galileo  verified  the  fal- 
lowing laws  of  falling  bodies: 

I.  The  velocity  attained  by  a  falling  body  is  propor- 
tional to  the  time  of  falling. 

II.  The  distance  fallen  is  proportional  to  the  square  of 
the  time  of  descent. 

III.  The  acceleration  is  twice  the  distance  a  body  falls 
in  the  first  second. 

These  laws  will  be  recognized  as  identical  with  those 
derived  for  uniformly  accelerated  motion,  §§  106  and  107. 
If  the  inclined  plane  in  Galileo's  experiment  be  tilted  up 
steeper,  the  effect  will  be  to  increase  the  acceleration  down 
the  plane  ;  and  if  the  board  be  raised  to  a  vertical  position, 
the  ball  will  fall  freely  under  gravity  and  the  acceleration 
will  become  #  (§  136). 

Since  the  acceleration  g  is  sensibly  constant  for  small 
distances  above  the  earth's  surface,  the  equations  already 
obtained  for  uniformly  accelerated  motion  may  be  applied 
directly  to  falling  bodies,  by  substituting  g  for  a  in  Equa- 
tions 5  and  6.  Thus  we  have 

v  =  gt^     .     .      .      (Equation  11) 
and  *  =  \  yt2 .     .     .     (Equation  12) 


LAWS   OF  FALLING   BODIES  131 


FIGURE  125.  —  YOSEMITE  FALL. 


132  MECHANICS   OF  SOLIDS 

If  in  Equation  12  t  is  one  second,  s=  \g\  or  the  dis- 
tance a  body  falls  from  rest  in  the  first  second  is  half  the 
acceleration  of  gravity.  A  body  falls  490  cm.  or  16.08  ft. 
the  first  second ;  and  the  velocity  attained  is  980  cm.  or 
32.16  ft.  per  second. 

142.  Projection  Upward.  — When  a  body  is  thrown  verti- 
cally upward,  the  acceleration  is  negative,  and  it  loses 
each  second  g  units  of  velocity  (980  cm.  or  32.16  ft.). 
Hence,  the  time  of  ascent  to  the  highest  point  is  the  time 
taken  to  bring  the  body  to  rest.  If  the  velocity  lost  is  g 
units  a  second,  the  time  required  to  lose  v  units  of  velocity 
will  be  the  quotient  of  v  by  #,  or 

, .         /i  velocity  of  projection  upward 

time  of  ascent  —  —     — y          .  — r • 

acceleration  oj~  gravity 

In  symbols  t  =  -   .      .     .     .     (Equation  13) 

9 

For  example,  if  the  velocity  of  projection  upward  were 
1470  cm.  per  second,  the  time  of  ascent,  neglecting  the 
frictional  resistance  of  the  air,  would  be  -Vg7^,  or  1.5  sec- 
onds. This  is  the  same  as  the  time  of  descent  again  to 
the  starting  point ;  hence,  the  body  will  return  to  the  start- 
ing point  with  a  velocity  equal  to  the  velocity  of  projection  but 
in  the  opposite  direction.  In  this  discussion  of  projection 
upward,  the  resistance  of  the  air  is  neglected. 

Problems 

Unless  otherwise  stated  in  the  problem,  g  is  to  be  taken  as  980  cm.- 
or  32  ft.-per-second  per  second. 

1.  The  tower  of  Pisa  is  180  ft.  high.  In  what  time  would  a  ball 
dropped  from  the  top  reach  the  ground?  With  what  velocity  would 
it  strike? 


CENTRIPETAL   AND   CENTRIFUGAL  FORCE        133 

2.  From  what  height  must  a  ball  fall  to  acquire  a  velocity  of 
1  km.  per  second  ? 

3.  With  what  velocity  in  a  vertical  direction  must  a  shell  be  fired 
just  to  reach  an  aeroplane  flying  at  an  elevation  of  one  mile? 

4.  A  ball  is  fired  vertically  with  an  initial  velocity  of  500  m.  per 
second.     Neglecting  the  resistance  of  the  air,  to  what  height  will  it 
rise,  and  in  what  time  will  it  return  to  the  earth  ? 

5.  An  aeroplane  flying  westward  with  a  velocity  of  60  mi.  per 
hour  and  at  an  elevation  of  one  mile,  dropped  a  bomb  while  vertically 
over  a  cathedral.     How  far  from  the  cathedral  did  the  bomb  strike 
the  ground  and  in  which  direction  ? 

6.  A  ball  fired  horizontally  reaches  the  ground  in  4  sec.     What 
was  the  height  of  the  point  from  which  it  was  fired? 

7.  A  cannon  ball  is  fired  horizontally  from  a  fort  at  an  elevation 
of  122.5  m.  above  the  neighboring  sea.     How  many  seconds  before  it 
will  strike  the  water  ? 

8.  The  Washington  monument  is  555  ft.  high.     Two  balls  are 
dropped  from  its  top  one  second  apart.     How  far  apart  will  the  balls 
be  when  the  first  one  strikes  the  ground  ? 

9.  An  iron  ball  was  dropped  from  an  aeroplane  moving  eastward 
at  the  rate  of  45  mi.  per  hour.     It  reached  the  ground  528  ft.  east  of 
the  vertical  line  through  the  point  from  which  it  was  dropped.    What 
was  the  elevation  of  the  aeroplane  ? 

10.  A  body  slides  without  friction  down  an  inclined  plane  300  cm. 
long  and  24.5  cm.  high.  If  it  moves  40  cm.  during  the  first  second, 
what  is  the  computed  value  of  g  ? 

VI.  CENTRIPETAL  AND  CENTRIFUGAL  FORCE 

143.   Definition    of    Centripetal  and    Centrifugal    Force.— 

Attach  a  ball  to  a  cord  and  whirl  it  around  by  the  hand. 
The  ball  pulls  on  the  cord,  the  pull  increasing  with  the 
velocity  of  the  ball.  If  the  ball  is  replaced  by  a  heavier 
one,  with  the  same  velocity  the  pull  is  greater.  If 'a  longer 
cord  is  used,  the  pull  is  less  for  the  same  velocity  in  the 
.circle. 


134  MECHANICS   OF  SOLIDS 

The  constant  putt  which  deflects  the  body  from  a  rectilinear 
path  and  compels  it  to  move  in  a  curvilinear  one  is  the  cen- 
tripetal force. 

The  resistance  which  a  body  offers  on  account  of  its  inertia, 
to  deflection  from  a  straight  line  is  the  centrifugal  force. 
When  the  motion  is  uniform  and  circular,  the  force  is  at 
right  angles  to  the  path  of  the  body  around  the  circle  and 
constant. 

These  two  forces  are  the  two  aspects  of  the  stress  in  the 
cord  (third  law  of  motion),  the  action  of  the  hand  on  the 
ball,  and  the  reaction  of  the  ball  on  the  hand. 

144.  Value  of  Either  Force  —  The  centripetal  acceleration 

Q 

for  uniform  circular  motion  (§  110)  is  a  =  — ,  where  v  is 

T 

the  uniform  velocity  in  the  circle,  and  r  is  the  radius. 
Further,  in  §  130  the  relation  between  force  and  accelera- 
tion was  found  to  be  as  follows:  force  equals  the  product 
of  the  mass  and  the  acceleration  imparted  to  it  by  the  force. 
Hence  we  have 

centripetal  force  =  mass  x  centripetal  acceleration, 
or  /=— .'     .     .     .     (Equation  14) 

This  relation  gives  the  value  of  either  the  centripetal 
or  the  equal  centrifugal  force  in  the  absolute  system  of 
measurement,  because  it  is  derived  from  the  laws  of  motion 
and  is  independent  of  gravity.  In  the  metric  system  m 
must  be  in  grams,  v  in  centimeters  per  second,  and  r  in 
centimeters ;  f  is  then  in  dynes.  To  obtain  f  in  grams  of 
force,  divide  by  980  (§  115).  In  the  English  system,  m 
must  be  in  pounds,  v  in  feet  per  second,  and  r  in  feet ; 
dividing  by  32.2,  the  result  will  be  in  pounds  of  force. 


CENTRIFUGAL  FORCE. 

Above  :  Auto  Race  on  a  Circular  Raised  Track. 

Below :  Sled  in  Swiss  Winter  Sports  being  thrown  over  the  embank- 
ment by  centrifugal  force. 


ILLUSTRATIONS    OF   CENTRIFUGAL    FORCE       135 

For  example  :  If  a  mass  of  200  g.  is  attached  to  a  cord  1  m.  long 
and  is  made  to  revolve  with  a  velocity  of  140  cm.  per  second,  the  ten- 


sion in  the  cord  is  20°  X  14°2  =  39,200  dynes  =  =  40  grams  of 

f  100  980 

force. 

Again  if  a  body  having  a  mass  of  10  Ib.  1  oz.  move  in  a  circle  of 
5  ft.  radius  with  a  velocity  of  20  ft.  per  second,  then  the  centripetal 

force  is/=  10rV  *  2<>2  =  25  pounds  of  force. 
5  x  32.2 

145.  Illustrations  of  Centrifugal  Force.  —  Water  adhering  to 
the  surface  of  a  grindstone  leaves  the  stone  as  soon  as  the  centrifugal 
force,  increasing  with  the  velocity,  is  greater  than  the  adhesion  of  the 
water  to  the  stone.  Grindstones  and  flywheels  occasionally  burst  when 
run  at  too  high  a  speed,  the  latter  when  the  engine  runs  away  after  a 
heavy  load  is  suddenly  thrown  off.  When  the  centripetal  force 
ceases  to  deflect  the  body  from  the  tangent  to  the  circle,  the  body 
flies  off  along  the  tangent  line.  A  stone  is  thrown  by  whirling  it  in 
a  sling  and  releasing  one  of  the  strings. 

A  carriage  or  an  automobile  rounding  a  curve  at  high  speed  is  sub- 
ject to  strong  centrifugal  forces,  which  act  through  the  tires.  The 
centripetal  force  consists  solely  of  the  friction  between  the  tires  and 
the  ground.  If  the  friction  is  insuffi- 
cient, "  skidding  "  takes  place. 

When  a  spherical  vessel  containing 
some  mercury  and  water  is  rapidly 
whirled  on  its  axis  (Fig.  126),  both  the 
mercury  and  the  water  rise  and  form 
separate  bands  as  far  as  possible  from 
the  axis  of  rotation,  the  mercury  out- 

FIGURE  126.  —  WHIRLING  LIQUIDS. 
Centrifugal   machines  are  used   in 

sugar  refineries  to  separate  sugar  crystals  from  the  sirup,  and  in  dye- 
works  and  laundries  to  dry  yarn  and  wet  clothes  by  whirling  them 
rapidly  in  a  large  cylinder  with  openings  in  the  side.  Honey  is  ex- 
tracted  from  the  comb  in  a  similar  way.  When  light  and  heavy  par- 
ticles are  whirled  together,  the  heavier  ones  tend  toward  the  outside. 
New  milk  is  an  emulsion  of  fat  and  a  liquid,  and  the  fat  globules  are 
lighter  than  the  liquid  of  the  emulsion.  Hence,  when  fresh  milt  is 
whirled  in  a  dairy  separator,  the  cream  and  the  milk  form  distinct 
layers  and  collect  in  separate  chambers. 


136 


MECHANICS  OF  SOLIDS 


VII.    THE  PENDULUM 

146.  Simple  Pendulum.  —  Any  body  suspended  so  as  to 
swing  about  a  horizontal  axis  is  a  pendulum.  A  simple 
pendulum  is  an  ideal  one.  It  may  be  denned  as  a  material 
particle  without  size  suspended  by  a  cord  without  weight. 
A  small  lead  ball  suspended  by  a  long  thread  without  sen- 
sible mass  represents  very  nearly  a  simple  pendulum. 
When  at  rest  the  thread  hangs  vertically  like  a  plumb 
line;  but  if  the  ball  be  drawn  aside  and  released,  it  will 
oscillate  about  its  position  of  rest.  Its  oscillations  become 
gradually  smaller ;  but  if  the  arc  described  be  small,  the 
period  of  its  swing  will  remain  unchanged. 

This  feature  of  pendular  motion  first  attracted  the 
attention  of  Galileo  while  watching  the  slow  oscillations  of 
a  "  lamp  "  or  bronze  chandelier,  suspended  by  a  long  rope 
from  the  roof  of  the  cathedral  in  Pisa.  Galileo  noticed 
the  even  time  of  the  oscillations  as  the 
path  of  the  swinging  chandelier  became 
shorter  and  .  shorter.  Such  a  motion, 
which  repeats  itself  over  and  over  in 
equal  time  intervals,  is  said  to  be  periodic. 


147.  The  Motion  of  a  Pendulum.  —  A N  in 

Fig.  127  is  a  nearly  simple  pendulum  with  the 
ball  at  N.  When  the  ball  is  drawn  aside  to  the 
position  B,  its  weight,  represented  by  BG,  may  be 
resolved  into  two  components,  BD  in  the  direc- 
tion of  the  thread,  and  BC  at  right  angles  to  it 
and  tangent  to  the  arc  BNE.  The  latter  is  the 
force  which  produces  motion  of  the  ball  toward  N. 
As  the  ball  moves  from  B  toward  N  the  component  BC  becomes 
smaller  and  smaller  and  vanishes  at  N,  where  the  whole  weight  of  the 
batt  is  in  the  direction  of  the  thread.  In  falling  from  B  to  N,  the 
ball  moves  in  the  arc  of  a  circle  under  the  influence  of  a  force  which 
is  greatest  at  B  and  becomes  zero  at  TV.  The  motion  is  therefore 


FIGURE  127.— 
FORCES  ACTING  ON  A 
PENDULUM. 


THE  MOTION   OF  A   PENDULUM 


137 


INTERIOR  OF  PISA  CATHEDRAL. 

The  bronze  chandelier  which  Galileo  observed  hangs  just  in  front  of  the 

altar. 


138  MECHANICS   OF  SOLIDS 

accelerated  all  the  way  from  B  to  N,  but  not  uniformly.     The  velocity 
increases  continuously  from  B  to  N,  but  at  a  decreasing  rate. 

The  ball  passes  N  with  its  greatest  velocity  and  continues  on  toward 
E.  From  N  to  E  the  component  of  the  weight  along  the  tangent 
which  is  always  directed  toward  N,  opposes  the  motion  and  brings  the 
pendulum  to  rest  at  E.  It  then  retraces  its  path  and  continues  to 
oscillate  with  a  periodic  and  pendular  motion. 

148.  Definition  of  Terms. — The  center  of  suspension  is  the 
point  or  axis  about  which  the  pendulum  swings.     A  single 

vibration  is  the  motion  comprised  between 
two  successive  passages  of  the  pendulum 
through  the  lowest  point  of  its  path,  as  the 
motion  from  Nio  B  (Fig.  128)  and  back 
to  N  again.  A  complete  or  double  vibration 
is  the  motion  between  two  successive  pas- 
sages of  the  pendulum  through  the  same 
point  and  going  in  the  same  direction.  A 
complete  vibration  is  double  that  of  a 
single  one.  The  period  of  vibration  is  the 
FIGURE  128.—  time  consumed  in  making  a  complete  or 
SIMPLE  PENDU-  double  vibration.  The  amplitude  is  the 

LUM 

arc  BN  OT  the  angle  BAN. 

149.  Laws  of  the  Pendulum.  —  The  following  are  the  laws 
of  a  simple  pendulum  which  are  independent  of  both  the 
material  and  the  weight: 

I.  For  small  amplitudes,  the  period  of  vibration  is 
independent  of  the  amplitude. 

'  II.    The  period  of  vibration  is  proportional  to  the  square 
root  of  the  length  of  the  pendulum. 

III.  The  period  of  vibration  is  inversely  proportional  to 
the  square  root  of  the  acceleration  of  gravity. 

One  of  the  earliest  and  most  important  discoveries  by 
Galileo  was  that  of  the  experimental  laws  of  the  motion  of 


CENTER   OF  OSCILLATION 


139 


a  pendulum,  made  when  he  was  about  twenty  years  of  age. 
This  was  long  before  their  theoretical  investigation. 

If  the  period  of  a  single  vibration  of  a  simple  pendulum 
is  denoted  by  f,  the  length  by  Z,  and  the  acceleration  of 
gravity  by  g,  it  can  be  shown  that 


t  =  TTV/-.     .     .     .     (Equation  15) 


To  illustrate  Law  I.  It  is  only  necessary  to  count  the  vibrations  of 
a  pendulum  which  take  place  in  some  convenient  time  with  different 
amplitudes.  Their  number  will  be  found  to  be  the 
same.  This  result  will  hold  even  when  the  ampli- 
tudes are  so  small  that  the  vibrations  can  only  be  ob- 
served with  a  telescope. 

To  illustrate  Law  II.  Mount  three  pendulums  (Fig. 
129),  making  the  lengths  1  m.,  \  m.,  and  ^  m.  re- 
spectively. Observe  the  period  of  a  single  vibra- 
tion for  each.  They  will  be  1  sec.,  £  sec.,  and  % 
sec.  nearly,  or  in  periods  proportional  to  the  square 
root  of  the  lengths. 

In  accordance  with  Law  III  a  pendulum 
oscillates  more  slowly  on  the  top  of  a  high 
mountain  than  at  sea  level,  and  more 
slowly  at  the  equator  than  at  the  poles. 
Place  a  strong  magnet  just  under  the  bob 
of  the  longest  pendulum,  which  must  be 
iron.  It  will  then  be  found  to  vibrate  in 
a  slightly  shorter  period  than  before.  The 
downward  magnetic  pull  on  the  bob  is 
equivalent  to  an  increased  value  of  g. 

150.  Center  of  Oscillation.  —  Insert 
a  small  staple  in  one  end  of  a  meter  stick, 
and  suspend  it  so  as  to  swing  as  a  pendulum  about  a 
horizontal  axis  through  the  staple  (Fig.  130).  With  a 
ball  and  a  thread  make  a  simple  pendulum  that  will  vi- 
brate in  the  same  period  as  the  meter  stick.  Beginning  at 
the  staple,  lay  oft'  on  the  meter  stick  the  length  of  this 


FIGURE  129. 
—  PENDULUMS 
OF  DIFFERENT 
LENGTHS. 


FIGURE 
1  30.  - 

C  ENTER 

OF     OS- 
CILLATION. 


140  MECHANICS  OF  SOLIDS 

pendulum.  It  will  extend  two  thirds  of  a  meter  down.  Bore  a  hole 
through  the  meter  stick  at  the  point  thus  found,  and  suspend  it  as  a 
pendulum  by  means  of  a  pin  through  this  hole.  Its  period  of  vibration 
will  be  the  same  as  before. 

The  bar  is  a  compound  pendulum,  and  the  new  axis  of 
vibration  is  called  the  center  of  oscillation.  The  distance 
between  the  center  of  suspension  and  the  center  of  oscilla- 
tion is  the  length  of  the  equivalent  simple  pendulum  that 
vibrates  in  the  same  period  as  the  compound  pendulum. 
The  centers  of  suspension  and  of  oscillation  are  inter- 
changeable without  change  of  period. 

151.  Center  of  Percussion.  —  Suspend  the  meter  bar  by  the  staple 
at  the  end  and  strike  it  with  a  soft  mallet  at  the  center  of  oscillation. 
It  will  be  set  swinging  smoothly  and  without  perceptible  jar. 

Hold  a  thin  strip  of  wood  a  meter  long  and  four  or  five  centimeters 
wide  by  the  thumb  and  forefinger  near  one  end.  Strike  the  flat  side 
with  a  soft  mallet  at  different  points.  A  point  may  be  found  where 
the  blow  will  not  throw  the  wood  strip  into  shivers,  but  will  only  set 
it  swinging  like  a  pendulum. 

The  center  of  oscillation  is  also  called  the  center  of  per- 
cussion; if  the  suspended  body  be  struck  at  this  point  at 
right  angles  to  the  axis  of  suspension,  it  will  be  set  swing- 
ing without  jar.  A  baseball  club  or  a  cricket  bat  has  a 
center  of  percussion,  and  it  should  strike  the  ball  at  this 
point  to  avoid  breaking  the  bat  and  "  stinging  "  the  hands. 

152.  Application  of  the  Pendulum.  —  Galileo's  discovery 
suggested  the  use  of  the  pendulum  as  a  timekeeper.     In 
the  common  clock  the  oscillations  of  the  pendulum  regulate 
the  motion  of  the  hands.     The  wheels  are  kept  in  motion 
by  a  weight  or  a  spring,  and  the  regulation  is  effected  by 
means  of  the  escapement  (Fig.  131).     The  pendulum  rod, 
passing  between  the  prongs  of  a  fork  a,  communicates  its 
motion  to  an  axis  carrying  the  escapement,  which  ter- 


QUESTIONS  AND  PROBLEMS 


141 


minates  in  two  pallets  n  and  m.  These  pallets  engage 
alternately  with  the  teeth  of  the  escapement  wheel  72,  one 
tooth  of  the  wheel  escaping  from  a  pallet 
every  double  vibration  of  the  pendulum. 
The  escapement  wheel  is  a  part  of  the 
train  of  the  clock  ;  and  as  the  pendulum 
controls  the  escapement,  it  also  controls 
the  motion  of  the  hands. 

153.  Seconds  Pendulum.  —  A  seconds  pen- 
dulum is  one  making  a  single  vibration  in 
a  second.  Its  length  in  New  York  is 
99.31  cm.  This  is  the  length  of  the 
equivalent  simple  pendulum  vibrating  sec- 
onds. The  value  of  gravity  g  increases 
from  the  equator  to  the  poles,  and  the 
length  of  the  seconds  pendulum  increases 
in  the  same  proportion,  s 

Questions  and  Problems 

1.  Why  can   a   heavy  shot    be   thrown    much 
farther  by  swinging  it  from  the  end  of  a  short  wire 
or  cord  than  by  hurling  it  from  the  shoulder  as  in 
"  putting  the  shot  "  ? 

2.  Why  is  the  outer  rail  on    a  railway    curve 
elevated  above  the  inner  one  ? 

3.  A  ball  weighing  10  Ib.  is  attached  to  a  cord  2  ft.   long  and  is 
whirled  about  the  hand  at  the  rate  of  ten  revolutions  in  three  seconds. 
What  is  the  tension  in  the  cord  ? 

4.  A  ball  swings  as  a  conical  pendulum;    its   mass   is  2  kg.,  its 
distance  from   the  center  of  its   circular  path   is   30  cm.,    and   it 
makes  ten    revolutions   in   35   seconds.     What   horizontal   force   in 
grams  would  be  necessary  to  hold  the  ball  at  any  point  in  its  path 
if  it  were  not  revolving  ? 

5.  Find  the  period  of  vibration  of  a  pendulum  70  cm.  long,  the 
value  of  g  being  980  cm.-per-second  per  second. 


FIGURE  131.  —  Es- 
CAPEMENT. 


142  MECHANICS   OF   SOLIDS 

6.  Calculate  the  length  of  a  seconds  pendulum  at  a  place  where 
the  value  of  g  is  980  cm.-per-second  per  second. 

7.  At  a  place  where  g  is  32  ft.-per-second  per  second  what  is  the 
length  of  a  pendulum  that  vibrates  in  £  sec.  ? 

8.  What  would  be  the  acceleration  of  gravity  if  a  pendulum  one 
meter  long  had  a  period  of  vibration  of  one  second  ? 

9.  If  a  simple  pendulum  90  cm.  long  makes  64  single  vibrations 
per  minute,  what  is  the  value  of  </? 

10.  Two  balls  of  the  same  diameter  but  of  different  materials  and 
masses  are  suspended  by  threads  of  the  same  length  and  of  negligible 
mass.  If  made  to  vibrate  as  pendulums,  will  their  periods  of  vibra- 
tion differ  and  why  ? 


CHAPTER   VI 

MECHANICAL  WORK 
I.   WORK  AND  ENERGY 

154.  Work.  —  A  man  does  work  in  climbing  a  hill  by  lifting 
himself  against  the  pull  of  gravity ;  a  horse  does  work  in  drawing  a 
wagon  up  an  inclined  roadway ;  a  locomotive  does  work  in  hauling 
a  train  on  the  level  against  frictional  resistances ;  gravity  does  work 
against  the  inertia  of  the  mass  when  it  causes  the  weight  of  a  pile 


THE  LARGEST  AND  MOST  POWERFUL  LOCOMOTIVE  IN  THE  WORLD. 

driver  to  descend  with  increasing  velocity ;  steam  does  work  on  the 
piston  of  a  steam  engine  and  moves  it  by  pressure  against  a  resist- 
ance; the  electric  current  does  work  by  means  of  a  motor  when  it 
drives  an  air  compressor  on  an  electric  car  and  forces  air  into  a  com- 
pression tank. 

Mechanical  work  means  the  overcoming  of  resistance. 
Unless  there  is  a  component  of  motion  in  the  direction  in 
which  the  force  acts  in  overcoming  the  resistance,  no 
work  in  a  physical  sense  is  done.  The  columns  in  a  mod- 
ern steel  building  do  no  work,  though  they  sustain  great 

143 


144  MECHANICAL    WORK 

weight ;  the  pillars  supporting  a  pediment  over  a  portico 
do  no  work ;  a  person  holding  a  weight  suffers  fatigue, 
but  does  no  work  in  the  sense  in  which  this  word  is  used 
in  physics,  where  it  is  employed  to  describe  the  result 
accomplished  and  not  the  effort  made. 

155.  Measure  of  Mechanical  Work.  —  Mechanical  work  is 
measured  by  the  product  of  the  force  and  the  displace- 
ment of  its  point  of  application  in  the  direction  in  which 
the  force  acts,  or 

work  =  force  x  displacement. 
In  symbols  w=fx  s.     .     v    >     (Equation  16) 

Since  force  is  equal  to  the  product  of  mass  and  accelera- 
tion (§  130), 

w  =  ma  x  8.     .     .     .     (Equation  17) 

156.  Units  of  Work.  —  Before  use  can  be  made  of  these 
expressions  for  work,  it  is  necessary  to  define  the  units 
employed  in  measuring  work.'     Three  or  four  such  units 
are  in  common  use  : 

1.  The  foot  pound  (ft.  lb.),  or   the  work  done  by  a 
pound  of  force  working  through  a  space  of  one  foot.     If 
a   pound    weight  is   lifted  a  foot   high,  or  if   a  body  is 
moved  a  distance  of  one  foot  by  a  force  of  one  pound,  a 
foot  pound  of  work  is  done.     This  unit  is  in  common  use 
among  English-speaking   engineers.     It   is   open   to   the 
objection  that  it  is  variable,  since  a  pound  of  force  varies 
with  the  latitude  and  with  the  elevation  above  sea  level. 

2.  The  kilogram  meter  (kg.  m.),  or  the  work  done  by 
a   kilogram   of   force  working   through   a   space   of   one 
meter.      It  is  the  gravitational  unit  of  work  in  the  metric 
system,  and  varies  in  the  same  manner  as  the  foot  pound. 
The  gram-centimeter  is  also  used  as  a  smaller  gravitational 


POWER  145 

unit  of  work.  The  kilogram  meter  is  equal  to  100,000 
gram-centimeters. 

3.  The  erg,1  or  the  work  done  by  a  dyne  working 
through  a  distance  of  one  centimeter.  The  erg  is  the 
absolute  unit  in  the  c.  g.  8.  system  and  is  invariable. 

Since  a  gram  of  force  is  equal  to  980  dynes  (§  115),  if 
a  gram  mass  be  lifted  vertically  one  centimeter,  the  work 
done  against  gravity  is  980  ergs.  Hence  one  kilogram 
meter  is  equal  to  980  x  1000  x  100  =  98,000,000  ergs. 

The  mass  of  a  "nickel"  is  5  g.  The  work  done  in  lifting  it 
through  a  vertical  distance  of  5  m.  is  the  continued  product  of  5,  500, 
and  980,  or  2,450,000  ergs.  The  erg  is  therefore  a  very  small  unit 
and  not  suitable  for  measuring  large  quantities  of  work.  For  such 
purposes  it  is  more  convenient  to  use  a  multiple  of  the  erg,  called  the 
joule.2  Its  value  is 

1  joule  =  107  ergs  =  10,000,000  ergs. 

Expressed  in  this  larger  unit,  the  work  done  in  lifting  the 
"  nickel "  is  0.245  joule.8 

157.  Power.  —  While  it  takes  time  to  do  work,  it  is 
plain  that  time  is  not  an  element  in  the  amount  of  work 
done.  To  illustrate :  Suppose  a  ton  of  marble  is  lifted 
by  a  steam  engine  out  of  a  marble  quarry  300  ft.  deep. 
The  work  is  done  by  means  of  a  wire  rope,  which  the 
engine  winds  on  a  drum.  If  now  the  drum  be  replaced 
by  another  of  twice  the  diameter,  and  running  at  the 
same  rate  of  rotation,  the  ton  of  marble  will  be  lifted  in 
half  the  time ;  but  the  total  work  done  against  gravity 
remains  the  same,  namely,  600,000  ft.  Ib. 

In  an  important  sense  the  engine  as  an  agent  for  doing 
work  is  twice  as  effective  in  the  second  instance  as  in  the 


1  The  erg  is  from  the  Greek  word  meaning  work. 

2  From  the  noted  English  investigator  Joule. 

8  The  joule  is  equal  to  about  f  of  a  foot  pound. 


MECHANICAL    WORK 

first.  Time  is  an  essential  element  in  comparing  the 
capacities  of  agents  to  do  work.  Such  a  comparison  is 
made  by  measuring  the  power  of  an  agent.  Power  tells 
us  not  how  much  work  is  done,  but  how  fast  it  is  done. 


A  MARBLE  QUARRY. 
Power  is  the  time  rate  of  doing  work,  Or 


power  =          =£*J. 

time          t 


(Equation  18) 


This  expression  may  be  used  directly  to  measure  power, 
due  regard  being  paid  to  the  units  employed.  The  result 
will  be  in  foot  pounds  per  second,  kilogram  meters  per 
second,  gram-centimeters  per  second,  or  ergs  per  second, 
according  to  the  consistent  units  used. 

The  units  of  power  universally  used  by  engineers  are 


GIANT  ORE  CRANE. 

When  these  jaws  close,  as  shown  in  the  picture  on  page  153,  the  bucket 
holds  12  tons  of  iron  ore. 

either  the   horse  power  or  the  watt  and  its  multiple  the 
kilowatt. 

The  horse  power  (H.P.)  is  the  rate  of  working  equal 
to  33,000  ft.  Ib.  per  minute,  or  to  550  ft.  Ib.  per  second. 


148  MECHANICAL    WORK 

Hence 


in  which  /is  in  pounds  of  force,  8  in  feet,  and  t  in  seconds. 
In  the  c.  g.  s.  system  the  watt  1  is  the  rate  of  working 
equal   to   one   joule  per  second.     A  kilowatt  (K.W.)    is 
1000  watts. 


Hence     watts  =       xs^  ;  K.W.  =       *  *   •     (Equation  20) 

In  Equation  20  /  is  in  dynes,  s  in  centimeters,  and  t 
in  seconds. 

One  horse  power  equals  746  watts,  or  0.746  kilowatt 
(nearly  -|  K.  W.).  To  convert  kilowatts  into  horse  powers 
approximately,  add  one  third  ;  to  convert  horse  powers 
into  kilowatts,  subtract  one  fourth.  For  example,  60  K.W. 
are  equal  to  80  H.P.,  and  100  H.P.  are  equal  to  75  K.W. 

The  power  capacity  of  direct  current  dynamo  electric  generators  is 
now  universally  expressed  in  kilowatts  ;  the  steam  engines  and  water 
turbines  used  to  drive  these  generators  are  commonly  rated  in  the  same 
unit  of  power;  so,  too,  the  capacity  of  electric  motors  is  more  often 
given  in  kilowatts  than  in  horse  powers.  A  kilowatt  hour  means  power 
at  the  rate  of  a  kilowatt  expended  for  one  hour.  Thus,  20  kilowatt 
hours  mean  20  K.W.  for  one  hour,  or  5  K.W.  for  four  hours,  etc. 

158.  Energy.  —  Experience  teaches  that  under  certain 
conditions  bodies  possess  the  capacity  for  doing  work. 
Thus,  a  body  of  water  at  a  high  level,  gas  under  pressure 
in  a  tank,  steam  confined  in  a  steam  boiler,  and  the  air 
moving  as  a  wind,  are  all  able  to  do  work  by  means  of 
appropriate  motors.  In  general,  a  body  or  system  on  which 
work  has  been  done  acquires  increased  capacity  for  doing 
work.  It  is  then  said  to  possess  more  energy  than  before. 


1  From  the  noted  English  engineer  James  Watt. 


POTENTIAL   ENERGY 


149 


"  Work  may  be  considered  as  the  transference  of  energy 
from  one  body  or  system  to  another."  "  Energy  we  know 
only  as  that  which  in  all  natural  phenomena  is  constantly 
passing  from  one  portion  of  matter  to  another."  Since 
the  work  done  on  a  body^is  the  measure  of  its  increase 
of  energy,  work  and  energy  are  measured  in  the  same 
units. 

159.  Potential  Energy.  —  A  mass  of  compressed  air  in 
an  air  gun  tends  to  expand ;  it  possesses  energy  and  may 
expend  it  in  propelling  a  bullet. 
Energy  is  stored  also  in  the  lifted 
weight  of  the  pile  driver  (Fig. 
132),  the  coiled  spring  of  the 
clock,  the  bent  bow  of  the  archer, 
the  impounded  waters  behind  a 
dam,  the  chemical  changes  in  a 
charged  storage  battery,  and  the 
mixed  charge  of  gasoline  vapor 
and  air  in  the  cylinder  of  a  gas 
engine. 

In  all  such  cases  of  the  storage 
of  energy  a  stress  (§  43)  is  pres- 
ent. The  compressed  air  pushes 
outward  in  the  air  gun ;  gravity 
pulls  on  the  lifted  weight;  the  FIGURE  132.  — PILE  DRIVER. 
spring  tends  to  uncoil  in  the  clock ;  the  bent  bow  tries  to 
unbend ;  the  water  presses  against  the  dam  ;  the  electric 
pressure  is  ready  to  produce  a  current ;  and  the  explosive 
gas  mixture  awaits  only  a  spark  to  set  free  its  energy. 
The  energy  thus  stored,  which  is  associated  with  a  stress  or 
with  a  position  with  respect  to  some  othe  body,  is  energy 
of  stress,  or,  more  commonly,  potential  energy.  The  energy 
of  an  elevated  body,  of  bending,  twisting,  of  chemical  sep- 


150  MECHANICAL    WORK 

aration,  and  of  air,  steam,  or  water  under  pressure,  are  all 
examples  of  potential  energy. 

160.  Kinetic  Energy.  —  A  body  also  possesses  energy  in 
consequence  of  its  motion ;  the  energy  of  a  moving  body 
is  known  as  kinetic  energy.  The.  descending  hammer  forces 
the  nail  into  the  wood,  the  rushing  torrent  carries  away 
bridges  and  overturns  buildings  ;  the  swiftly  moving  can- 
non ball,  by  virtue  of  its  high  speed,  demolishes  fortifica- 
tions or  pierces  the  steel  armor  of  a  battleship  ;  the  energy 
stored  in  the  massive  rotating  flywheel  keeps  the  engine 
running  and  may  do  work  after  the  steam  is  shut  off. 
When  the  engine  is  speeding  up,  it  pushes  and  pulls  on 
the  shaft  to  increase  the  speed  of  the  flywheel ;  in  other 
words,  the  engine  does  work  on  the  flywheel.  After 
normal  speed  has  been  reached,  all  the  work  done  by  the 
engine  goes  into  the  driven  machinery;  but  if  an  extra 
load  comes  on  the  engine,  its  speed  does  not  drop  sud- 
denly, because  it  is  sustained  by  the  flywheel  giving  out 
some  of  its  stored  energy  to  help  along  the  engine.  The 
engine  tends  to  stop  the  flywheel,  and  this  now  does  work 
instead  of  absorbing  energy. 

When  a  meteoric  body,  or  "  shooting  star,"  enters  the 
earth's  atmosphere,  its  energy  of  motion  is  converted  into 
heat  by  friction  with  the  air ;  the  heat  generated  raises 
the  temperature  of  the  meteor  (at  least  on  its  surface) 
until  it  glows  like  a  star.  If  it  is  small,  it  may  even  burn 
up  or  become  fine  powder. 

The  energy  of  the  invisible  molecular  motions  of  bodies 
constituting  heat  is  included  under  kinetic  energy  no  less 
than  that  of  their  visible  motion.  Heat  is  a  form  of 
kinetic  energy. 

Kinetic  energy  must  not  be  confused  with  force.  A 
mass  of  moving  matter  carries  witli  it  kinetic  energy,  but 


KINETIC  ENERGY  151 

it  exerts  no  force  until  it  encounters  resistance.  Energy 
is  then  transferred  to  the  opposing  body,  and  force  is 
exerted  only  during  the  transfer. 

161.  Measure  of  Energy.  —  Energy  is  measured  in   the 
same  terms  as  those  used  in  measuring  work.     In  general, 
potential  energy  is  the  measure  of  the  mechanical  work 
done  in  storing  the  energy,  or 

P.E.=fxs.    .     .     (Equation  21) 

If  /  is  in  pounds  of  force  and  8  in  feet,  the  result  is  in 
foot  pounds.  Similarly,  if  /  is  in  grams  of  force  and  « 
in  centimeters,  the  potential  energy  is  expressed  in  gram- 
centimeters. 

Since  a  gram  of  force  is  equal  to  980  dynes,  expressed 

1  Tl    f^T^O^ 

P.E.  =  980  x  grams  x  centimeters. 

162.  Kinetic  Energy  in  Terms  of  Mass   and  Velocity.  — 

The  work  fs  done  by  the  force  /  on  the  mass  m  to  give  it 
the  velocity  v,  while  working  through  the  distance  «, 
measures  the  kinetic  energy  acquired,  or, 

K.E.  =f  x  s. 

But  it  is  highly  desirable  to  express  kinetic  energy  in 
terms  of  the  mass  m  and  the  acquired  velocity  t>,  instead 
of  /  and  s.  By  the  second  law  of  motion  (§  130)  /  =  ma. 
Hence  K.E.  =maxs.  But  s  =  \at^.  Therefore  K.E.  = 
±ma?t2.  Also  v  =  at  (§  106);  therefore 

K.E.  =  \mv*.   .     .     (Equation  22) 

Both  m  and  v  are  magnitudes  independent  of  gravitation ; 
it  follows  that  the  results  calculated  from  Equation  22  can- 
not be  in  gravitational  units.  If  m  is  expressed  in  grams 
and  v  in  centimeters  per  second,  the  kinetic  energy  is  in 


152  MECHANICAL    WORK 

ergs.  Since  the  gram -centimeter  is  equal  to  980  ergs,  to 
reduce  the  result  to  gram-centimeters,  divide  by  the  value 
of  g  in  this  system,  or  980. 

In  precisely  the  same  way,  if  m  is  in  pounds  and  v  in 
feet  per  second,  to  obtain  the  energy  in  foot  pounds, 
divide  by  the  value  of  g  in  the  English  system,  32.2. 

To  illustrate :  If  an  automobile,  weighing  3000  lb.,  is  running  at  a 
speed  of  30  miles  per  hour,  find  its  kinetic  energy. 

A  mile  a  minute  is  88  ft.  per  second,  and  30  miles  an  hour  or  half 
a  mile  a  minute  is  44  ft.  per  second.  Hence  the  kinetic  energy  of  the 

m°VingCari8  3000  x  44»      ml8fi,,, 

2x32.2    =  9°'186  ft  lb> 

This  energy  represents  very  nearly  the  work  required  to  lift  the  car 
30  ft.  high  against  gravity,  for  this  work  is 

3000  x  30  =  90,000  ft.  lb. 

A  large  ship,  moving  toward  a  wharf  with  a  motion  scarcely  per- 
ceptible, will  crush  with  great  force  small  intervening  craft.  The 
moving  energy  of  the  large  vessel  is  great  because  of  its  enormous 
mass,  even  though  its  velocity  is  small.  Its  weight  is  supported  by 
the  water  and  has  nothing  to  do  with  its  crushing  force. 

163.  Transformations  of  Energy.  —  When  a  bullet  is  shot 
vertically  upward,  it  gradually  loses  its  motion  and  its 
kinetic  energy,  but  gains  energy  of  position  or  potential 
energy.  When  it  reaches  the  highest  point  of  its  flight, 
its  energy  is  all  potential.  It  then  descends,  and  gains 
energy  of  motion  at  the  expense  of  energy  of  position. 
The  one  form  of  energy  is,  therefore,  convertible  into  the 
other. 

The  pendulum  illustrates  the  same  principle.  While 
the  bob  is  moving  from  the  lowest  point  of  its  path 
toward  either  extremity,  its  kinetic  energy  is  converted 
into  potential  energy ;  the  reverse  transformation  sets  in 


DISSIPATION  OF  ENERGY 


153 


when  the  pendulum  reverses  its  motion.  All  physical 
processes  involve  energy  changes,  and  such  changes  are 
in  ceaseless  progress. 

164.  Conservation  of  Energy.  —  Whenever  a  body  gains 
energy  as  the  result  of  work  done  on  it,  it  is  always  at  the 
expense  of  energy  in 

some  other  body  or 
system.  The  agent, 
or  body,  which  does 
work  always  loses 
energy ;  the  body 
which  has  work  done 
on  it  gains  energy 
equal  to  the  work 
done.  On  the  whole 
there  is  neither  gain 
nor  loss  of  energy, 
but  only  its  transfer 
from  one  body  to  an- 
other. Innumerable 
facts  and  observa- 
tions show  that  it  is 
as  inlpossible  to  cre- 
ate energy  as  it  is 
to  create  matter.  So 
the  law  of  conserva- 
tion of  energy  means  that  no  energy  is  created  and  none 
destroyed  by  the  action  of  forces  we  know  anything  about. 

165.  Dissipation  of  Energy.  —  Potential   energy   is   the 
more  highly  available  or  useful  form  of  energy.     It  always 
tends  to  go  over  into  the  kinetic  type,  but  in  such  a  way 
that  only  a  portion  of  the  kinetic  energy  is  available  to 
effect  useful  changes  in  nature  or  in  the  mechanic  arts. 


CLOSED  JAWS  OF  ORE  BUCKET. 

This  crane  makes  one  trip  per  minute  from 
the  hold  of  the  vessel  to  the  ore  train  on  the 
dock. 


154  MECHANICAL    WORK 

The  remainder  is  dissipated  as  heat.  This  running  down 
of  energy  by  passing  into  an  unavailable  form  is  known  as 
the  dissipation  of  energy.  It  was  first  recognized  and  dis- 
tinctly stated  by  Lord  Kelvin  in  1859. 

The  capacity  which  a  body  possesses  for  doing  work 
does  not  depend  on  the  total  quantity  of  energy  which  it 
may  possess,  but  only  on  that  portion  which  is  available, 
or  is  capable  of  being  transferred  to  other  bodies.  In  the 
problems  of  physics  our  chief  concern  is  with  the  varia- 
tions of  energy  in  a  body  and  not  with  its  total  value. 

Questions  and  Problems 

1.  A  cord  that  will  just  support  an  iron  ball  will  generally  break 
if  the  attached  ball  is  lifted  and  allowed  to  drop.     Explain.        , 

2.  In  what  form  is  the  energy  of  a  coiled  spring  ?     Of  a  bomb  ? 
Of  a  pile  driver? 

3.  Lake  Tahoe  in  the  Sierra  Nevadas  is  at  an  elevation  of  6225  ft. 
above  the  sea.    Account  for  the  energy  of  position  stored  there  in  the 
water. 

4.  Why  has  the  ball  in  leaving  the  gun  so  much  more  energy  of 
motion  than  the  gun  has  in  the  recoil  ? 

5.  Why  is  "  perpetual  motion  "  impossible  ? 

6.  Is  not  the  case  of  the  earth  going  around  the  sun  a  case  of 
perpetual  motion?     How  does  this  differ  from  what  is  commonly 
meant  by  "  perpetual  motion  "  ? 

7.  A  man  weighing  200  Ib.  climbs  to  the  top  of  a  hill  900  ft. 
high.     How  much  work  does  he  do  ? 

8.  A  man  carries  a  ton  of  coal  up  a  flight  of  stairs  14  ft.  high. 
How  much  work  does  he  do  ? 

9.  A  force  of  200  dynes  moves  a  mass  of  100  g.  through  a  dis- 
tance of  50  cm.     How  much  work  is  done  ? 

10.  A  load  of  two  tons  was  drawn  up  a  hill  half  a  mile  long  by  a 
traction  engine.  The  hill  was  100  ft.  high.  How  much  work  was 
done  ?  What  force  did  the  engine  exert  ? 

SUGGESTION.  —  Notice  that  the  work  done  by  the  engine  in  pulling  the 
load  half  a  mile  is  the  same  as  lifting  it  vertically  100  ft. 


Lord  Kelvin  (Sir  William  Thomson),  1824-1907,  was  born 
at  Belfast.  He  graduated  at  Cambridge  in  1845  and  in  the  same 
year  received^the  appointment  of  professor  of  natural  philosophy 
in  the  University  of  Glasgow,  a  position  which  he  held  for  fifty- 
three  years.  He  was  one  of  the  greatest  mathematical  physicists 
of  his  day.  His  invention  of  the  astatic  mirror  galvanometer  and 
the  siphon  recorder  has  made  successful  marine  cables  a  reality. 
His  laboratory  for  the  use  of  students  was  the  first  of  the  kind  to 
be  established.  His  most  noteworthy  investigations  were  in  heat, 
energy,  and  electricity,  yet  there  is  scarcely  any  portion  of  physi- 
cal science  that  has  not  been  greatly  enriched  by  his  genius. 


WHAT  A  MACHINE  IS  155 

11.  How  much  work  can  a  40  H.P.  engine  do  in  an  hour?     How 
many  tons  of  coal  can  it  raise  out  of  a  mine  400  ft.  deep  in  10  hours  ? 

12.  Express  in  joules  the  work  done  by  a  force  of  100  kg.  in  mov- 
ing 100  kg.  through  a  distance  of  100  km. 

13.  An  electric  motor  rated  at  100  K.W.  is  used  to  operate  a  pump. 
The  water  has  to  be  raised  100  m.     How  many  liters  will  it  be  pos- 
sible to  pump  per  hour  ? 

14.  The  mass  of  a  railroad  train  is  250  tons,  and  the  resistan.ee  to  its 
motion  on  a  level  track  is  15  Ib.  per  ton.     What  H.P.  must  the  loco- 
motive develop  to  maintain  a  speed  of  40  miles  per  hour  on  the  level  ? 

15.  What  is  the  potential  energy  of  a  stone  weighing  100  Ib.  as  it 
rests  on  the  top  of  a  column  50  ft.  high  ?    What  will  be  its  kinetic 
energy  at  the  moment  of  reaching  the  ground  if  it  should  fall  ?    How 
much  work  would  be  done  in  placing  the  stone  back  on  the  column  ? 

16.  A  ball  with  a  mass  of  100  g.  is  given  a  velocity  of  100  m.  per 
sec.  by  being  struck  with  a  club.     What  was  the  energy  of  the  blow  ? 

17.  An  automobile  weighing  2500  Ib.  when  running  at  the  rate  of  30 
mi.  an  hour  strikes  a  telephone  pole.    Calculate  the  energy  of  the  blow. 

18.  A  force  of  100  g.  moves  a  mass  1000  g.  through  a  distance  of 
100  m.  in  10  sec.     Express  the  activity  of  the  agent  in  watts. 

19.  The  mass  of  the  ram  of  a  certain  pile  driver  is  2000  Ib.     It 
falls  from  a  height  of  20  ft.  upon  the  head  of  a  pile  and  drives  it  2  ft. 
into  the  ground.     What  is  the  energy  of  the  blow  delivered  to  the 
pile  ?     What  is  the  resistance  offered  by  the  ground  ? 

20.  A  cannon  ball  weighing  10  Ib.  is  fired  from  a  cannon  whose 
barrel  is  5  ft.  long  with  a  velocity  of  1500  ft.  per  sec.     Calculate  the 
momentum  of  the  ball ;  also  the  energy  of  the  ball ;  also  the  average 
force  acting  on  the  ball  in  the  barrel. 

II.     MACHINES 

166.  What  a  Machine  is. — A  machine  is  a  device  designed 
to  change  the  direction  or  the  value  of  a  force  required  to 
do  useful  work,  or  one  to  transform  and  transfer  energy. 

Simple  machines  enable  us  to  do  many  things  that  would  be  impos- 
sible for  us  to  do  without  them.  A  boy  can  draw  a  nail  with  a  claw 


156  MECHANICAL   WORK 

hammer  (Fig.  133)  ;  without  it  and  with  his  fingers  alone  he  could 
not  start  it  in  the  least.  By  the  use  of  a  single  pulley,  the  direction 
of  the  force  applied  may  be  changed,  so  as  to  lift  a 
weight,  for  example,  while  the  force  acts  in  any 
convenient  direction.  Two  men  can  easily  lift  a 
piano  up  to  a  second  story  window  with  a  rope  and. 
tackle.  Perhaps  the  mosfimportant  use  of  machines 
is  for  the  purpose  of  utilizing  the  forces  exerted  by 
animals,  and  by  wind,  water,  steam,  or  electricity. 
A  water  wheel  transforms  the  potential  and  kinetic 

FIGURE   133  energy  of  falling  water  into  mechanical  energy  rep- 

HAMMER  AS  LEVER,  resented  by  the  energy  of  the  rotating  wheel.  A 
dynamo  electric  machine  transforms  mechanical 
energy  into  the  energy  of  an  electric  current,  and  an  electric  motor 
at  a  distance  transforms  the  electric  energy  back  again  into  useful 
mechanical  work. 

167.  General  Law  of  Machines.  —  Every  machine  must 
conform  to  the  principle  of  the  conservation  of  energy  ; 
that  is,  the  work  done  by  the  applied  force  equals  the  work 
done  in  overcoming  the  resistance,  except  that  some  of  the 
applied   energy  may  be  dissipated  as  heat  or  may   not 
appear  in  mechanical  form.     A  machine  can  never  produce 
an  increase  of  energy  so  as  to  give  out  more  than   it 
receives. 

Denote  the  applied  force,  or  effort,  by  E  and  the  resist- 
ance by  R,  and  let  D  and  d  denote  the  distances  respectively 
through  which  they  work.  Then  from  the  law  of  conser- 
vation of  energy,  the  effort  multiplied  by  the  distance 
through  which  it  acts  is  equal  to  the  resistance  multiplied 
by  its  displacement,  or 

ED  =  Rd.    .    .    .    (Equation  23) 

168.  Friction.  —  Friction  is  the  resistance  which  opposes  an 
effort  to  slide  or  roll  one  body  over  another.     It  is  called  into 
action  whenever  a  force  is  applied  to  make  one  surface 


FRICTION 


157 


move  over  another.  Friction  arises  from  irregularities  in 
the  surfaces  in  contact  and  from  the  force  of  adhesion. 
It  is  diminished  by  polishing  and  by  the  use  of  lubricants. 
Experiments  show  that  friction  (a)  is  proportional  to 
the  pressure  between  the  surfaces  in  contact,  (5)  is  inde- 


MACHINE  FOR  MEASURING  FRICTION  AT  MASS.  INST.  OF  TECHNOLOGY. 

pendent  of  the  area  of  the  surfaces  in  contact  within  cer- 
tain limits,  and  (c)  has  its  greatest  value  just  before 
motion  'takes  place.  The  friction  of  a 
solid  rolling  on  a  smooth  surface  is 
less  than  when  it  slides.  Advantage 
is  taken  of  this  fact  to  reduce  the  fric- 
tion of  bearings.  A  ball-bearing  (Fig. 
134)  substitutes  the  rolling  friction 
between  balls  and  rings  for  the  sliding  FlGURE  134  _  B 
friction  between  a  shaft  and  its  journal.  BEARING. 


158 


MECHANICAL    WORK 


FIGURE  135.  —  ROLLER  BEARING. 


Roller  bearings  (Fig. 
135)  are  also  used  with 
similar  advantages. 

169.  Advantages  and 
Disadvantages  of  Friction. 
—  Friction  has  innumer- 
able uses  in  preventing 
motion  between  surfaces 
in  contact.  Screws  and 
nails  hold  entirely  by 
friction ;  we  are  able  to  walk  because  of  friction  between 
the  shoe  and  the  pavement ;  shoes  with  nails  in  the  heels  are 
dangerous  on  cast-iron  plates  because  the  friction  between 
smooth  iron  surfaces 
is  small.  Friction  is 
useful  in  the  brake 
to  stop  a  motor  car 
or  railway  train,  in 
holding  the  driving 
wheels  of  a  locomo- 
tive to  the  rails,  and 
in  enabling  a  gaso- 
line engine  to  drive 
an  automobile  by 
friction  between  the 
tires  and  the  street. 
On  the  other  hand, 
friction  is  also  a  re- 
sistance opposing 
useful  motion,  and 

Whenever    motion  CATERPILLAR  TRACTOR. 

takes      place,       work    The  chain  beit  around  the  wheels  greatly  in- 
must  be  done  against  creases  the  friction  with  the  ground. 


SIMPLE  MACHINES  159 

this  frictional  resistance.  The  energy  thus  consumed  is 
converted  into  heat  and  is  no  longer  available  for  useful 
work. 

170.  Efficiency  of  Machines.  —  On  account  of  the  impos- 
sibility of  avoiding  friction,  every  machine  wastes  energy. 
The  work  done  is,  therefore,  partly  useful  and  partly  waste- 
ful. The  efficiency  of  a  machine  is  the  ratio  of  the  useful 
work  done  by  it  to  the  total  work  done  by  the  acting  force, 

or  efficiency  =    ^  work  done 

total  energy  applied 

For  example,  an  effort  of  100  pounds  of  force  applied  to  a  machine 
produces  a  displacement  of  40  ft.  and  raises  a  weight  of  180  Ib.  20  ft. 
high.  Then  100  x  40  =  4000  ft.  Ib.  of  energy  are  put  into  the  ma- 
chine, and  the  work  done  is  180  x  20  =  3600  ft.  Ib. 


Hence  efficiency  =          =  Q.9  =  90  per  cent. 

Ten  per  cent  of  the  energy  is  wasted  and  ninety  per  cent  recovered. 

Since  every  machine  wastes  energy,  a  machine  which 
will  do  either  useful  or  useless  work  continuously  without 
a  supply  of  energy  from  without,  a  so-called  "perpetual 
motion  machine,"  is  thus  clearly  impossible. 

Let  e  denote  the  efficiency  of  a  machine;  then  from  the 
relations  just  explained,  Equation  23  becomes 

eED  =  Ed.     .     .     .     (Equation  24) 

This  relation  is  the  strictly  correct  one  to  apply  to  all 
machines;  but  in  most  problems  dealing  with  simple 
machines,  friction  is  neglected. 

171.  Simple  Machines.  —  All  machines  can  be  reduced  to 
six  mechanical  powers  or  simple  machines:  the  lever,  the 
pulley,  the  inclined  plane,  the  wheel  and  axle,  the  wedge, 
and  the  screw.  Since  the  wheel  and  axle  is  only  a  modi- 


160  MECHANICAL    WORK 

fied  lever,  and  the  wedge  and  the  screw  are  modifications 
of  the  inclined  plane,  the  mechanical  powers  may  be  re- 
duced to  three. 

In  solving  problems  relating  to  simple  machines  in  ele- 
mentary physics  it  is  customary  to  neglect  friction  and  to 
consider  that  the  parts  of  machines  are  rigid  and  without 
weight.  With  these  limitations,  the  law  expressed  by 
Equation  23  holds  good. 

172.  Mechanical  Advantage.  —  A  man  working  a  pump 
handle  and  pumping  water  is  an  agent  applying  energy ; 
the  pump  and  the  water  compose  a  system  receiving  energy. 
In  a  simple  machine  the  force  exerted  by  the  agent  ap- 
plying energy,  and  the  opposing  force  of  the  system  re- 
ceiving energy,  may  be  denoted  by  the  two  terms,  effort, 
E,  and   resistance,  R.     The  problem  in  simple  machines 
consists   in   finding   the    ratio    of    the    resistance   to   the 
effort. 

The  ratio  of  the  resisting  force  R  to  the  applied  force  E 
is  called  the  mechanical  advantage  of  the  machine.  This 
ratio  may  always  be  expressed  in  terms  of  certain  parts  of 
simple  machines. 

173.  Moment  of  *,  Force. — In   the   application   of   the 
lever,  the  pulley,  or  the  wheel  and  axle  there  is  motion 
about  an  axis.     The  application  of  a  single  force  to  a  body 
with  a  fixed  axis  produces  rotation  only.     Examples  are  a 
door  swinging  on  its  hinges  and  the  flywheel  of  an  engine. 

The  effect  of  a  force  in  producing  rotation  depends,  not 
only  on  the  value  of  the  force,  but  on  the  distance  of  its 
line  of  application  from  the  axis  of  rotation.  A  smaller 
force  is  required  to  close  a  door  when  it  is  applied  at  right 
angles  to  the  door  at  the  knob  than  when  it  is  applied 
near  the  hinge.  Also,  an  increase  in  the  speed  of  rota- 
tion of  a  flywheel  may  be  secured  either  by  increasing  the 


THE  LEVER 


161 


F 


FIGURE  136  —  MO- 
MENT OF  FORCE. 


applied  force  or  by  lengthening  the  crank.  Both  these 
elements  of  effectiveness  are  included  in  what  is  known  as 
the  moment  of  a  force. 

The  moment  of  a  force  is  the  product  of 
the  force  and  the  perpendicular  distance 
between  its  line  of  action  and  the  axis  of 
rotation.  Let  M  be  a  body  which  may 
rotate  about  an  axis  through  0  (Fig. 
136).  The  moment  of  the  force  F  ap- 
plied at  B  in  the  direction  CB  is  F  x  OB ; 
applied  in  the  direction  AB,  its  moment 
is  Fx  OA.  The  point  0  is  called  the 
center  of  moments. 

A  moment  is  considered  positive  if  it  produces  rotation 
in  a  clockwise  direction,  and  negative  if  in  the  other.  If 
the  sum  of  the  positive  moments  equals  that  of  the  negative 
moments,  there  is  equilibrium. 

The  principle  of  moments  is  a  very  useful  one  in  solv- 
ing a  great  variety  of  problems. 

c  174.  The  Lever.  —  The  lever 

^|  I  is  more  frequently  used  than 

any  other  simple  machine.     In 

E*  I  *B        its  simplest  form  the  lever  is  a 

rigid  bar  turning  about  a  fixed 
axis  called  the  fulcrum.  It  is 
convenient  to  divide  levers  into 
three  classes,  distinguished  by 
the  relative  position  of  the  ful- 
crum with  respect  to  the  two 
forces.  In  the  first  class  the 
fulcrum  is  between  the  effort 
E  and  the  resistance  R  (Fig.  137)  ;  in  the  second  class 
the  resistance  is  between  the  effort  and  the  fulcrum  ;  in 


FIGURE  137.  —  LEVERS. 


162 


MECHANICAL    WORK 


FIGURE  138.  —  LEVER, 
FIRST  CLASS. 


the  third  class  the 
effort  is  between 
the  resistance  and 
the  fulcrum. 


FIGURE  139. -LEVER, 
SECOND  CLASS. 


FIGURE    140.  —  SCIS- 
SORS. 


175.   Examples  of  Levers. — A  crowbar 
used  as  a  pry  (Fig.  138)  is  a  lever  of  the  first 

class,  but  when  used  to  lift  a  weight  with  one 
end  on  the  ground  (Fig.  139),  it  is  a  lever  of  the 
second   class.     Scissors    (Fig.   140)    are   double 
levers  of  the  first 
class.      So    also 
are  the   tongs  of 

a  blacksmith,  and  those  used  in  chemi- 
cal laboratories  for  lifting  crucibles 
(Fig.  141).  The  forearm  when  it  supports  a  weight  in  the  extended 

hand  (Fig.  142),  and  the  door  when 
it  is  closed  by  pushing  it  near  the 
hinge,  are  examples  of  levers  of  the 
third  class. 
Nut  -  crack- 
ers (Fig. 
143)  and 


FIGURE  141. — TONGS. 


FIGURE  142.  —  FOREARM  AS  LEVER. 


FIGURE  143.  —  NUT 
CRACKER. 


lemon  squeezers  are  double  levers  of  the  second 
class. 

The  steelyard  (Fig.  144)  is  a  lever  of  the  first  class  with  unequal 
arms.  The  common  balance  (Fig.  145)  is  a  lever  of  the 
first  class  with  equal  arms.  The  two  weights  are  thus 
also  equal.  The  conditions  for  a  sensitive  balance,  to 

show    a    small   excess    of 
weight   in    one   pan    over 
^^^  that  in  the  other,  are  small 

friction  at  the  fulcrum,  a  light  beam,  and 
the  center  of  gravity  only  slightly  lower 
than  the  "  knife-edge  "  forming  the  f ul- 


176.    Mechanical  Advantage  of  the  Lever.  —  In 

STEELYARD.    Fig.  146  U  is  the  effort,  R  the  resistance  or 


MECHANICAL  ADVANTAGE  OF  THE  LEVER       163 


weight  lifted,  O  the  fulcrum,  and  AC  and  BO  the  lever 
arms.  Consider  the  lever  to  be  weightless  and  to  rotate 
about  O  without  fric- 
tion; then  the  moment 
of  the  force  E  about 
the  fulcrum  (§  173)  is 
E  x  A  0,  and  that  of  the 
force  R  is  R  x  BO. 
These  two  forces  tend  to 
produce  rotation  in  op- 
posite directions  ;  for 
equilibrium  their  mo- 
ments are  therefore  FlGURE  145. -COMMON  BALANCE. 
equal,  that  is,  ExAO=RxBO',  from  which 


E     BO 

(Equation  25) 

Hence,  the  mechanical 
advantage  of  the  lever 
equals  the  inverse  ratio 

FIGURE  146.  —  MECHANICAL  ADVANTAGE  OF    of  its  arins. 

LEVER-  If  the  weight  of  the 

lever  has  to  be  taken  into  account,  it  is  to  be  treated  as  a 
force  acting  at  the  center 
of  gravity  of  the  lever,  and    CZ 
its  moment  must  be  added 
to  that  of  the  force  turning 
the  lever  in  the  same  direc- 
tion as  its  own  weight. 

EXAMPLE.     The  weights  W^ 
and  W2  are  placed  at  distances 
5  and  8  units  respectively  from  0  (Fig.  147).     If  Wl  is  20  lb.,  what 
mustW2  be  for  equilibrium?    By  the  principle  of  moments  about  O, 


[  U  Jb 

rrr 


FIGURE  147. 


164  MECHANICAL    WORK 

20  x  5  =  Wz  x  8 ; 
whence  W2  =  12.5  Ib. 

If  the  lever  is  uniform,  it  is  balanced  about  the  fulcrum  0  and  its 
moment  is  zero.  Suppose  the  weight  of  the  bar  to  be  1  Ib.  and  its 
center  of  gravity  4  units  to  the  left  of  0.  The  equation  for  equi- 
librium would  then  be 

20  x  5  +  1  x  4  =  W2  x  8. 
Whence  ^  =  13  lb> 

177.  The  Wheel  and  Axle  consists  of  a  cylinder  and  a 
wheel  of  larger  diameter  usually  turning  together  on  the 
same  axis.  In  Fig.  148  the  axle  passes  through  (7,  the 
radius  of  the  cylinder  is  BO,  and  that  of  the  wheel  is 
AC.  The  weights  P  and  W  are  sus- 
pended by  ropes  wrapped  around  the  cir- 
cumference of  the  two  wheels;  their 
moments  about  the  axis  0  are  P  x  AO 
and  Wx  BO  respectively.  For  equilib- 
rium these  moments  are  equal,  that  is, 
PxAC=  WxBO.  Hence, 


FIGURE    148.-  J?=±^=:il.     (Equation  26) 

WHEEL  AND   AXLE.  P       BO        r 


R  and  r  are  the  radii  of  the  wheel  and  the  axle  respec- 
tively. The  weight  P  represents  the 
effort  applied  at  the  circumference  of 
the  wheel,  and  the  weight  W  the  resist- 
ance at  the  circumference  of  the  axle. 
Therefore,  the  mechanical  advantage  of 
the  wheel  and  axle  is  the  ratio  of  the 
radius  of  the  wheel  to  that  of  the  axle. 

178.    Applications.  —  The  old  well   wind- 
lass for  drawing  water  from  deep  wells  (Fig.    FIGURE     149.  —  WELL 
149)  by  means  of  a  rope  and  bucket  is  an  ap-  WINDLASS. 


TEE  PULLEY 


165 


plication  of  the  principle  of  the  wheel 
and  axle.  In  the  windlass  a  crank  takes 
the  place  of  a  wheel  and  the  length  of 
the  crank  is  the  radius  of  the  wheel. 

In  the  capstan  (Fig.  150)  the  axle  is 
vertical,  and  the  effort  is  applied  by 
means  of  handspikes  inserted  in  holes 
in  the  top. 

The  derrick  (Fig.  151)  is  a  form  of 
wheel  and  axle  much  used  for  raising 


FIGURE  150.  —  CAPSTAN 


FIGURE  151.  —  DERRICK. 


heavy  weights.  In  the  form  shown 
it  is  essentially  a  double  wheel 
and  axle.  The  axle  of  the  first  sys- 
tem works  upon  the  wheel  of  the 
second  by  means  of  the  spur  gear. 
The  mechanical  advantage  of  such  a 
compound  machine  is  the  ratio  of  the 
product  of  the  radii  of 
the  wheels  to  the  product 
of  the  radii  of  the  axles. 
In  the  case  of  gearing, 
the  number  of  teeth  is 
substituted  for  the  ra- 
dius. 

179.  The  Pulley  consists  of  a  wheel,  called  a 
sheave,  free  to  turn  about  an  axle  in  a  frame, 
called  a  block  (Fig.  152). 
The  effort  and  the  resist- 
ance are  attached  to  a  rope  — BLOCK  AND 
which  moves  in  a  groove  cut  SHEAVE- 
in  the  circumference  of  the  wheel.  A 
simple  fixed  pulley  is  one  whose  axis 
does  not  change  its  position  ;  it  is  used 
to  change  the  direction  of  the  applied 
force  (Fig.  153).  If  friction  and  the 

FIGURE    153.-  SINGLE  rigidity  of  the  r°Pe  are  neglected,  the 
PULLEY.  tension  in  the  rope  is  everywhere  the 


FIGURE  152. 


w 


166 


MECHANICAL    WORK 


PRACTICAL  USE  OF  DERRICKS. 

These  enormous  derricks  are  used  for  raising  the  huge  blocks  of  marble 
from  the  quarry. 

same ;  the  effort  and  the  resistance  are 
then  equal  to  each  other  and  the 
mechanical  advantage  is  unity. 

In  the  movable  pulley  (Fig.  154)  it 
is  evident  that  the  weight  W  is  sup- 
ported by  two  parts  of  the  cord,  one 
half  of  it  by  means  of  the  hook  fixed 
in  the  beam  above  and  the  other  half 
by  the  effort  E  applied  at  the  free  end 
of  the  cord.  If  the  weight  is  lifted,  it 
rises  only  half  as  fast  as  the  cord 
travels. 

180.   Systems   of    Fixed   and    Movable 


W 


FIGURE    154.  —  MOV- 


ABLE PULLEY.         Pulleys.  —  Fixed   and  movable  pulleys 


MECHANICAL  ADVANTAGE  OF  SIMPLE  PULLEY     167 


are  combined  in  a  great  variety  of  ways.  The  most  com- 
mon is  the  one  employing  a  continuous  cord  with  one  free 
end  and  the  other  attached  to  a  rigid 
support  or  to  one  of  the  blocks.  Figure 
155  represents  a  combination  of  one  fixed 
and  one  movable  pulley.  Figure  156  il- 
lustrates the  common  "  block  and  tackle," 
where  each  block  has  more  than  one  sheave. 
181.  Mechanical  Advantage  of  the  Simple 
Pulley.  —  In  Fig.  157  the  cord  passes  in 
succession  around  each  pulley.  It  is  evi- 
dent that  if  the  movable 
pulley  and  the  resistance 
W  are  moved  toward  the  FIGURE  155  — 
fixed  pulley  a  distance  #,  FIXED  AND  Mov- 
each  cord  passing  between  ABLE  PULLEYS- 
the  two  blocks  must  be  shortened  by  a 
units.  The  effort  E  therefore  travels 
through  a  distance  of  na  units,  n  being  the 
number  of  parts  to  the  cord  between  the 
two  pulleys.  Then  by  the  general  law  of 
machines  (§  167), 


x  na  =  W X  a; 


whence 


W 


(Equation  27) 


Hence,  when  a  continuous  cord  is.  used^  the 
mechanical  advantage  of  the  pulley  is  equal 
FIGURE  156. —    to  the  number  of  times  the  cord  passes  to 
BLOCKANDTACKLE.     ^  from  the  movable  block. 

It  should  be  noticed  that  n  is  equal  to  the  entire  num- 
ber of  sheaves  in  the  fixed  and  movable  blocks,  or  to  that 


168 


MECHANICAL    WORK 


number  plus  one.  If  the  upper  block  in 
Fig.  157  were  the  movable  one,  that  is,  if 
the  system  were  inverted,  so  that  the  effort 
E  is  upward,  n  would  be  equal  to  one  more 
than  the  number  of  sheaves. 

182.  The  Differential  Pulley.  —  The  differ- 
ential pulley  (Fig.  158)  is  much  used  for 
lifting  heavy  machinery  by  means  of  a  rela- 
tively small  force. 
In  the  upper  block 
are  two  sheaves  of 
different  diameters 
turning  rigidly  to- 
gether. The  lower 
block  has  only  one 
sheave.  An  end- 
less chain  runs  over 
the  three  sheaves 
in  succession.  It 
is  kept  from  slip- 
ping by  projections  on  the  sheaves, 

which  fit  between  the  links  of  the 

chain.     A  practical  advantage  of 

the    differential    pulley    is    that 

there  is  alwaj7s  enough  friction  to 

keep  the  weight  from   dropping 

when  there  is  no  force  applied  to 

the  chain. 


FIGURE  157. — 
MULTIPLE  PUL- 
LEYS. 


The  mechanical  advantage  of  the  dif- 
ferential pulley  may  be  found  as  follows : 
In  Fig.  159,  which  is  an  outline  drawing 
of  this  pulley,  let  the  radius  A  C  of  the    FIGURE 
larger  sheave  be  denoted  by  R,  and  that 


\J 

158.  —  DIFFERENTIAL 
PULLEY. 


TEE  INCLINED  PLANE 


169 


of  the  smaller  one  A  B  by  r.  Suppose  a  force  E  to  move  the  chain  some 
convenient  distance  as  R  ;  then  a  length  r  winds  off  the  smaller  sheave 
at  B  and  a  length  R  winds  on  the  larger  sheave  at 
D.  The  length  of  chain  between  the  two  blocks  is 
thus  shortened  by  a  length  R  —  r,  and  the  weight  W  D 
is  lifted  a  distance  %(R  —  r).  The  work  done  by 
the  effort  E  is  E  x  R  and  the  work  dojie  on  W  is 
W  x  \(R  —  r).  Neglecting  friction,  these  expres- 
sions may  be  placed  equal  to  each  other,  or 


Whence 


W 
E 


R-r 


.     (Equation  28) 


Since  the  difference  R  —  r  may  be  made  small,  it  _ 

is  obvious  that  the  mechanical  advantage  of  the  dif-  OUTLINE  OF  DIF- 

ferential  pulley  is  large,  and  it  is  larger  the  nearer  r  FERENTIAL     PUL- 

approaches  R  in  length.  LEY. 

183.   The  Inclined  Plane.  —  Any  plane  surface  making  an 
angle  with  the  horizontal  is  an  inclined  plane.     Planks  or 


FIGURE  160.  —  HUGE  FLOATING  CRANE. 


170 


MECHANICAL    WOKK 


skids  used  to  roll  casks  and  barrels  up  to  a  higher  level  are 
examples  of  inclined  planes.  Every  road,  street,  or  railway 
not  on  a  level  is  an  inclined  plane.  The  steeper  the  incline, 
the  greater  the  push  required  to  force  the  load  up  the  grade. 
If  a  body  rests  on  an  inclined  plane  without  friction, 
the  weight  of  the  body  acts  vertically  downward,  while 
the  reaction  of  the  plane  is  perpendicular  to  its  surface, 
and  therefore  a  third  force  must  be  applied  to  maintain 
the  body  in  equilibrium  on  the  incline. 

184.   Mechanical  Advantage  of  the  Inclined  Plane.  —  Con- 
sider only  the  case  in  which  the  force  applied  to  maintain 

equilibrium  is  parallel  to  the 
face  of  the  plane  (Fig.  161). 
The  most  convenient  way 
to  find  the  relation  between 
the  force  E  and  the  weight 
JTof  the  body  D  is  to  apply 
the  principle  of  work  (§  167). 
Suppose  D  to  be  moved  by 
the  force  E  from  A  to  O.  Then  the  work  done  by  E  is 
E  x  AC.  Since  the  body  D  is  lifted  through  a  vertical  dis- 
tance BO,  the  work  done  on  it  against  gravity  is  Wx  EG. 
Therefore,  ExAC=  Wx  BO,  and 


(Equation  29) 


FIGURE  161.  —  INCLINED  PLANE. 


E     BC 


or  the  mechanical  advantqge,  when  the  effort  is  applied  parallel 
to  the  face  of  the  plane,  is  the  ratio  of  the  length  of  the  plane 
to  its  height. 

185.  Grades.  —  The  grade  of  an  inclined  roadway  is  ex- 
pressed as  the  number  of  feet  rise  per  hundred  feet  along 
the  incline.  If  the  rise,  for  example,  is  3  feet  for  every 
100  feet  measured  along  the  roadway,  the  road  has  a  three 


GRADES 


171 


per  cent  grade.  The  grade  of  railways  seldom  exceeds 
2  per  cent,  but  county  roads  and  state  highways  may  have 
8  or  10  per  cent  grades.  Various  expedients  are  adopted 
for  the  purpose  of  lengthening  the  incline  on  roads  and 
railways  so  as  to  keep  the  grades  within  practical  limits. 


THE  GREAT  PYRAMID. 

The  huge  stones  of  which  the  pyramids  are  made  were  probably  raised  to 
their  great  height  by  inclined  planes. 

Zigzags  and  "  switchbacks "  are  common  expedients  for 
the  purpose. 

A  most  remarkable  inclined  railway  track  is  on  the 
northern  approach  to  the  St.  Gotthard  tunnel  in  Switzer- 
land. This  tunnel  reaches  a  culminating  elevation  of  3786 
feet.  In  at  least  one  instance  the  railway  forms  three  turns 
of  a  screw,  one  above  the  other,  each  turn  lying  partly 
on  the  face  of  the  mountain  and  partly  in  a  tunnel  cut 


172 


MECHANICAL    WORK 


FIGURE  162.  — THE  WEDGE. 


through  the  rock.  This  novel  grade  enables  the  road  to 
surmount  a  precipice  by  means  of  an  inclined  plane,  the 
necessary  length  of  which  was  secured  along  the  thread  of 
a  mammoth  screw. 

186.  The  Wedge  is   a  double  inclined   plane  with  the 
effort  applied  parallel  to  the  base  of  the  plane,  and  usually 
by  a  blow  with  a  heavy  body  (Fig.  162).     Although  the 

principle  of  the  wedge  is 
the  same  as  that  of  the 
inclined  plane,  yet  no  ex- 
act statement  of  its  me- 
chanical advantage  is  pos- 
sible, because  the  resistance 
has  no  definite  relation  to 

the  faces  of  the  planes,  and  the  friction  cannot  be  neglected. 

Many  cutting  instruments,  such  as  the  ax  and  the  chisel, 

act  on  the  principle  of  the  wedge  ; 

also  nails,  pins,  and  needles. 

187.  The  Screw  is   a  cylinder, 
on  the  outer  surface  of  which  is  a 
uniform  spiral  projection,  called 
the   thread.     The    faces    of    this 
thread  are  inclined  planes.     If  a 
long  triangular  strip  of  paper  be 

wrapped  around  a  pencil  (Fig.  163),  with  the  base  of  the 
triangle  perpendicular  to  the  axis  of  the  cylindrical  pencil, 

the  hypotenuse  of  the  triangle 
will  trace  a  spiral  like  the  thread 
of  a  screw. 

The  screw  (Fig.  164)  works  in 
a  block  called  a  nut,  on  the  inner 
surface  of  which  is  a  groove,  the 
THE  NUT.        exact  counterpart  of  the  thread. 


FIGURE  163.— THE  SCREW. 


FIGURE  164, 


APPLICATIONS  OF  THE  SCREW 


173 


FIGURE  165.  —  PITCH  OF  SCREW. 


The  effort  is   applied  at  the  end  of  a  lever   or   wrench, 

fitted  either  to  the  screw  or  to  the  nut.     When  either 

makes  a  complete  turn,  the  screw  or  the  nut  moves  through 

a  distance  equal  to  that  between  two  adjacent  threads, 

measured  parallel  to  the  axis 

of  the  screw  cylinder.     This 

distance,  s  in  Figure  165,  is 

called  the  pitch  of  the  screw. 

It  is  usually  expressed  as  the 

number  of  threads  to  the  inch 

or  to  the  centimeter. 

188.  Mechanical  Advantage  of 

the  Screw.  —  Since  the  screw  is  usually  combined  with  the 
lever,  the  simplest  method  of  finding 
the  mechanical  advantage  is  to  apply 
the  principle  of  work,  as  expressed  in  the 
general  law  of  machines  (§  167).  If  the 
pitch  be  denoted  by  s  and  the  resistance 
overcome  by  R,  then,  ignoring  friction, 
the  work  done  against  R  in  one  revolu- 
tion of  the  screw  is  R  x  s.  If  the  length 
of  the  lever  is  £,  the  work  done  by  the 
effort  JE  in  one  revolution  is  E  x  2  irl. 

Whence  E  x  27rl=R  x  s,  or 


FIGURE  166.  —  JACK- 
SCREW. 


:    =         .  (Equation  30) 
E        s 

Hence,  the   mechanical   advantage  of 

the  screw  equals  the  ratio  of  the  dis- 

tance  traversed  by   the   effort   in  one 

revolution  of  the  screw  to  the  pitch  of   FIGURE  167.  —  LETTER 

the  screw.  PRESS. 

189.   Applications  of  the  Screw.  —  The  jackscrew  (Fig.  166),  the 
letter  press  (Fig.  167),  the  vise  (Fig.  168),  the  two  blade  propeller  of  a 


174 


MECHANICAL    WORK 


FIGURE     168.  — 
THE  VISE. 


flying  machine,  and  the  two,  three,  or  four  blade  propeller  of  a  ship 
are  familiar  examples  of  the  use  of  a  screw.  The  rapid  rotation  cf 
the  propeller  blades  tends  to  push  backward  the  air 
in  the  one  case  and  the  water  in  the  other,  but  the 
inertia  of  the  fluid  medium  produces  a  reaction 
against  the  propeller  and  forces  the  vessel  forward. 
The  screw  propeller  pushes  against  the  fluid  and  so 
forces  itself  and  the  vessel  to  which  it  is  attached  in 
the  other  direction. 

An  important  application  of  the  screw,  though  not 
as  a  machine,  is  that  for  measuring  small  dimensions.  The  wire 
micrometer  (Fig.  169)  and  the  spherometer 
(Fig.  170)  are  instruments  for  this  pur- 
pose. In  both,  an  accurate  screw  has  a 
head  divided  into  a  number  of  equal 
parts,  100  for  example,  so  as  to  register 
any  portion  of  a  revolution.  If  the  pitch 
of  the  screw  is  1  mm.,  then  turning  the 
head  through  one  of  its  divisions  causes 
the  screw  to  move  parallel  to  its  axis 
0.01  mm.  All  wood  screws,  augers,  gimlets,  and  most  machine  screws 
and  bolts  are  right-handed,  —  that  is,  they 
screw  in  or  away  from  the  observer  by  turn- 
ing around  in  the  direction  of  watch  hands. 
An  example  of  a  left-handed  screw  is  the 
turnbuckle  (Fig.  171).  This  has  a  right- 
handed  screw  at  one  end  and  a  left-handed 
screw  at  the  other.  It  is  used  for  tightening 
tie  rods,  stays,  etc.  One  turn  of  the  buckle 
brings  the  rods  together  a  distance  equal  to 
twice  the  pitch  of  the  screws. 


FIGURE  169.  —  MICROMETER. 


FIGURE  170. — SPHEROME- 
TER. 


Questions  and  Problems 


1.  What  are  the  relative  positions  of  the  effort,  the  resistance, 
and  the  fulcrum  in  the  following :  the  lever  as  applied  to  the  jack- 
screw,  the  oar  of  a  boat  in  row- 
ing, the  claw  hammer  in  pull- 
ing a  nail,  and  a  bar  applied  to 
a  car  wheel  to  move  the  car?  FIGURE  171.  —  TURNBUCKLE. 


QUESTIONS  AND  PROBLEMS  175 

2.  In   which   direction  does   friction   on  the    rails   act  on   the 
wheels  of  a  locomotive?     On  those  of  a  freight  car?    Does  it  act  in 
the  same  direction  on  the  front  and  rear  wheels  of  an  automobile  ? 

3.  Calculate  the  efficiency  of  a  machine  that  lifts  a  weight  of  1000 
Ib.  a  distance  of  8  ft.  by  the  action  of  a  force  of  100  Ib.  through  100  ft. 

4.  A  motor  whose  efficiency  is  90  %  delivers  10  H.P.    What  must 
be  the  input  ? 

5.  In  a  system  of  pulleys  a  tension  of  100  Ib.  is  applied  to  the 
rope  and  the  rope  is  drawn  60  ft.,  while  a  weight  of  500  Ib.  is  lifted 
10  ft.     What  is  the  efficiency  of  the  system  ? 

6.  A  weight  of  100  Ib.  is  lifted  by  a  lever  of  the  second  kind. 
The  weight  is  placed  2  ft.  from  the  fulcrum  and  the  lever  is  12  ft. 
long.     What  force  is  necessary  ? 

7.  A  bar  4  m.  long  is  of  uniform  size  and  weighs  1  kg.  to  the  meter. 
A  weight  of  10  kg.  is  placed  at  one  end,  and  the  fulcrum  is  1  m.  from 
that  end.     What  weight  at  the  other  end  will  produce  a  balance  ? 

8.  In  order  to  lift  a  weight  of  500  Ib.  at  one  end  of  a  bar  15  ft. 
long,  a  weight  of  100  Ib.  is  used  at  the  other  end.     The  bar  is  of  uni- 
form size  and  weighs  25  Ib.     Where  must  the  fulcrum  be  placed  ? 

9.  The  axle  on  which  the  rope  wound  in  a  windlass  was  8  in.  in 
diameter.    The  crank  was  12  in.  long  and  the  weight  lifted  was  200  Ib. 
What  force  was  applied  ? 

10.  The  diameter  of  a  ship's  capstan  is  16  in.     What  force  must 
be  applied  to  each  of  two  handspikes  at  an  effective  distance  of  6  ft. 
to  turn  the  capstan  and  lift  an  anchor  weighing  2400  Ib.  if  the 
efficiency  of  the  machine  is  80  per  cent  ? 

11.  In  a  system  of  six  pulleys,  three  of  which  are  movable,  how 
many  kilograms  can  a  force  of  25  kg.  support  ? 

12.  A  jackscrew  was  used  to  lift  a  weight  of  200  Ib.     The  lever 
was  2  ft.  long  and  the  screw  had  4  threads  to  the  inch.     Assuming  an 
efficiency  of  100  96,  what  force  was  applied  at  the  end  of  the  handle? 

13.  The  radii  of  a  wheel  and  the  axle  are  5  ft.  and  5  in.  respec- 
tively.    It  was  found  that  a  force  of  100  Ib.  could  lift  a  weight  of 
960  Ib.     What  weight  would  100  Ib.  of  force  lift  if  there  were  no 
friction  ?     What  is  the  efficiency  of  the  machine  ? 

14.  If  the  front  sprocket  wheel  of  a  bicycle  contains  24  sprockets 
and  the  rear  one  8,  how  far  will  one  complete  turn  of  the  pedals  drive 
a  28  in.  wheel? 


CHAPTER   VII 


SOUND 
I.     WAVE  MOTION 

190.  Vibrations.  —  A  vibrating  body  is  one  which  re- 
peats its  limited  motion  at  regular  short  intervals  of  time. 
A  complete  or  double  vibration  is  the  motion  between  two 
successive  passages  of  the  moving  body  through  any  point 
of  its  path  in  the  same  direction. 

If  we  suspend  a  ball  by  a  long  thread  and  set  it  swinging  like  a 
common  pendulum,  it  will  return  at  regular  intervals  to  the  starting 
point.  If  we  set  the  ball  moving  in  a  circle, 
the  string  will  describe  a  conical  surface  and 
the  ball  will  again  return  at  the  same  inter- 
vals to  the  starting  point. 

191.  Kinds  of  Vibration.  —  Clamp  one 
end  of  a  thin  steel  strip  in  a  vise  (Fig.  172) ; 
draw  the  free  end  aside  and  release  it.  It 
will  move  repeatedly  from  D'  to  D"  and 
back  again.  The  shorter  or  thicker  the  strip, 
the  quicker  its  vibration ;  when  it  becomes 
like  the  prong  of  a  tuning  fork,  it  emits  a 
musical  sound. 


D'  D 


Vibrations  like  these  are  transverse. 
FIGURE  172.  —  VIBRATION  A  body  vibrates  transversely  when  the 
OF  STEEL  STRIP.  direction  of  the  motion  is  at  right  angles 
to  its  length.  The  strings  of  a  violin,  the  reeds  of  a 
cabinet  organ,  and  the  wires  of  a  piano  are  familiar  ex- 
amples. 

176 


TRANSVERSE   WAVES 


177 


Fasten  the  ends  of  a  long  spiral  spring  securely  to  fixed  supports 
with  the  spring  slightly  stretched.  Crowd  together  a  few  turns  of 
the  spiral  at  one  end  and 
release  them.  A  vibratory 
movement  will  travel  from 
one  end  of  the  spiral  to  the  FlGURE  173.  — VIBRATORY  MOTION  IN  SPRING. 
other,  and  each  turn  of  wire  will  swing  backward  and  forward  in  the 
direction  of  the  length  of  the  spiral  (Fig.  173), 

The  vibrations  of  the  spiral  are  longitudinal.  A  body 
vibrates  longitudinally  when  its  parts  move  backward  and 
forward  in  the  direction  of  its  length.  The  vibrations  set 
up  in  a  long  glass  tube  by  stroking  it  lengthwise  with  a 
damp  cloth  are  longitudinal ;  so  are  those  of  the  air  in  a 
trumpet  and  the  air  in  an  organ  pipe. 

192.  Wave  Motion.  —  Tie  one  end  of  a  soft  cotton  rope,  such 
as  a  clothesline,  to  a  fixed  support ;  grasp  the  other  end  and  stretch 
the  rope  horizontally.    Start  a  disturbance  by  an  up-and-down  motion 
of  the  hand.     Each  point  of  the  rope  will  vibrate  with  simple  har- 
monic motion  (§  112),  while  the  disturbance  will  travel  along  the  rope 
toward  the  fixed  end. 

This  progressive  change  of  form  due  to  the  periodic  vibra- 
tion of  the  particles  of  the  medium  is  a  wave.  The  particles 
are  not  all  in  the  same  phase  (§  112)  or  stage  of  vibration, 
but  they  pass  through  corresponding  positions  in  suc- 
cession. 

193.  Transverse   Waves.  —  A   small  camel's-hair  brush  is  at- 
tached to  the  end  of  a  long  slender  strip  of  clear  wood,  mounted  as 


FIGURE  174.  —  INSCRIBING  TRANSVERSE  WAVE. 

shown  in  Fig.  174,  which  was  made  from  a  photograph  giving  an 
oblique  view  of  the  apparatus.     The  brush  should  touch  lightly  the 


178 


SOUND 


paper  attached  to  the  narrow  board,  which  may  be  moved  in  a  straight 
line  against  the  guiding  strip.  Ink  the  brush  and  while  it  is  at  rest 
push  the  paper  along  under  it.  The  brush  will  mark  the  straight 
middle  line  running  through  the  curve  shown  in  the  figure.  Replace 
the  board  in  the  starting  position;  then  pull  the  strip  aside  and 
release  it.  Again  draw  the  board  under  the  brush  with  uniform 
motion.  This  time  the  brush  traces  the  curved  line. 

The  strip  of  wood  vibrates  at  right  angles  to  the  direc- 
tion of  motion  of  the  paper  with  a  simple  harmonic  motion 
(§112);  the  board  moves  with  a  uniform  rectilinear 
motion;  the  curve  is  a  simple  harmonic  curve.  It  is  the 
resultant  of  the  two  motions,  and  illustrates  a  transverse 
wave.  A  transverse  wave  is  one  in  which  the  vibration  of  the 
particles  in  the  wave  is  at  right  angles  to  the  direction  in 
which  the  wave  is  traveling. 

194.  To  Construct  a  Transverse  Wave.  —  Suppose  a  series  of 
particles,  originally  equidistant  in  a  horizontal  straight  line,  to 


1 

% 

c   T 

T 

H 

a  ]        ] 

I     t 

!  !  It 

y 

r 

m   ,    | 

1 

i 

rrti 

1 

» 

! 

i 

i 

i  j 

i 

i 

i 

i 

* 

i  « 

FIGURE  175.  —  POSITION  OF  PARTICLES  IN  WAVE. 

Vibrate  transversely  with  simple  harmonic  motion.  Let  Fig.  175 
represent  the  position  of  the  particles  at  some  particular  instant,  the 
displacement  of  each  one  from  the  straight  horizontal  line  being 
found  by  means  of  an  auxiliary  circle  as  in  §  112.  They  will  out- 
line a  transverse  wave.  At  g  the  particle  has  reached  its  extreme 
displacement  in  the  positive  direction  and  is  momentarily  at  rest; 
the  particle  at  s  has  reached  its  maximum  negative  displacement,  and 
is  also  at  rest.  The  particle  at  m  is  moving  in  the  positive  direction 


LONGITUDINAL    WAVE 


179 


with  maximum  velocity,  and  the  particles  a  and  y  with  maximum 
velocity  in  the  negative  direction.  If  the  wave  is  traveling  to  the 
right,  then  an  instant  later  the  displacement  of  g  will  have  diminished 
and  that  of  i  will  have  increased  to  a  maximum,  the  crest  having 
moved  forward  from  g  to  i  in  the  short  interval.  The  successive 
particles  of  the  wave  all  differ  in  phase  by  the  same  amount. 

195.    Longitudinal  Wave.  —  Place  a  lighted  candle  at  the  conical 
end  of  the  long  tin  tube  of  Fig.  176.     Over  the  other  end  stretch  a 


m, 


FIGURE  176.  —  WAVE  OF  COMPRESSION  IN  TUBE. 

piece  of  parchment  paper.  Tap  the  paper  lightly  with  a  cork  mallet; 
the  transmitted  impulse  will  cause  the  flame  to  duck,  and  it  may 
easily  be  blown  out  by  a  sharper  blow. 

The  air  in  the  tube  is  agitated  by  a  vibratory  motion, 
and  a  wave,  consisting  of  a  compression  followed  by  a 
rarefaction,  traverses  the  tube.  The  dipping  of  the  flame 
indicates  the  arrival  of  the  compression.  Each  particle 
of  air  vibrates  longitudinally  in  the  tube,  the  disturbance 
being  similar  to  that  of  the  vibrating  spiral. 


E 


A  C  E  G 

FIGURE  177.  —  PARTICLES  IN  WAVE  OF  COMPRESSION. 

Figure  177  illustrates  the  distribution  of  the  air  particles 
when  disturbed  by  such  a  longitudinal  wave  of  com- 
pressions and  rarefactions.  B^  D,  F,  etc.,  are  regions  of 
compressions ;  A,  C,  E,  etc.,  those  of  rarefaction.  The 


180  SOUND 

distances  of  the  different  points  of  the  curve  from  the 
straight  line  denote  the  relative  velocities  of  the  air 
particles.  The  greatest  velocity  forward  is  at  the  middle 
of  the  condensation,  as  at  B,  and  the  greatest  velocity 
backward  is  at  the  middle  of  the  rarefaction,  as  at  A. 
A  and  (7,  or  B  and  2>,  are  in  the  same  phase,  that  is,  in 
corresponding  positions  in  their  path. 

A  longitudinal  wave  is  one  in  which  the  vibrations  are 
backward  and  forward  in  the  same  direction  as  the  wave  is 
traveling. 

196.  Wave  Length.  — The  length  of  a  wave  is  the  distance 
from  any  particle  to  the  next  one  in  the  same  phase,  as 
from  a  to   y  (Fig.   175),  or  from   A  to   0  or  B  to  D 
(Fig.  177).     Since  the  wave  form  travels  from  a  to  y,  or 
from  A  to  (7,  during  the  time  of  one  complete  vibration  of 
a   particle,    it   follows   that   the   wave    length   is    also   the 
distance  traversed  by  the  wave  during  one  vibration  period. 

197.  Water  Waves.  —  One  of  the  most  familiar  examples  of 
transverse  waves  are  those  on  the  surface  of  water.     For  deep  water 


FIGURE  178.  —  WATER  WAVE. 

the  particles  describe  circles,  all  in  the  same  vertical  plane  containing 
the  direction  in  which  the  wave  is  traveling,  as  illustrated  in  Fig.  178. 
The  circles  in  the  diagram  are  divided  into  eight  equal  arcs,  and  the 
water  particles  are  supposed  to  describe  these  circles  in  the  direction 
of  watch  hands  and  all  at  the  same  rate ;  but  in  any  two  consecutive 
circles  their  phase  of  motion  differs  by  one  eighth  of  a  period,  that  is, 
the  water  particles  are  taken  at  such  a  distance  apart  that  each  one 
begins  to  move  just  as  the  preceding  one  has  completed  one  eighth 
part  of  its  orbit.  When  a  has  completed  one  revolution,  b  is  one 
eighth  of  a  revolution  behind  it,  c  two  eighths  or  one  quarter,  etc. 


SOURCE  OF  SOUND  181 

A  smooth  curve  drawn  through  the  positions  of  the  particles  in  the 
several  circles  at  the  same  instant  is  the  outline  or  contour  of  a  wave. 

When  a  particle  is  at  the  crest  of  a  wave,  it  is  moving  in  the  same 
direction  as  the  wave ;  when  it  is  in  the  trough,  its  motion  is  opposite 
to  that  of  the  wave. 

The  crests  and  troughs  are  not  of  the  same  size,  and  the  larger  the 
circles  (or  amplitude),  the  smaller  are  the  crests  in  comparison  with 
the  troughs.  Hence  the  crests  of  high  waves  tend  to  become  sharp  or 
looped,  and  they  break  into  foam  or  white  caps. 

II.  SOUND  AND  ITS  TRANSMISSION 

198.  Sound  may  be  defined  as  that  form  of  vibratory  mo- 
tion in  elastic  matter  which  affects  the  auditory  nerves,  and 
produces  the  sensation  of  hearing.     All  the  external  phenom- 
ena of   sound  may  be  present  without  any  ear  to  hear. 
Sound  should  therefore  be  distinguished  from  hearing. 

199.  Source  of  Sound.  —  If  we  suspend  a  small  elastic  ball  by  a 
thread  so  that  it  just  touches  the  edge  of  an  inverted  bell  jar,  and 
strike  the  edge  of  the  jar  with  a  felted  or  cork  mallet,  the  ball  will 
be  repeatedly  thrown  away  from  the  jar  as  long  as  the 

sound  is  heard.     This  shows  that  the  jar  is  vibrating 
energetically. 

Stretch  a  piano  wire  over  the  table  and  a  little  above 
it.  Draw  a  violin  bow  across  the  wire,  and  then  touch 
it  with  the  suspended  ball  of  the  previous  paragraph. 
So  long  as  the  wire  emits  soun^.  the  ball  will  be  thrown 
away  from  it  again  and  again. 

If  a  mounted  tuning  fork  (Fig.  179)  is  sounded,  and 
a  light  ball  of  pith  or  ivory,  suspended  by  a  thread,  is 
brought  in  contact  with  one  of  the  prongs  at  the  back,  FIGURE  179. 
it  will  be  briskly  thrown  away  by  the  energetic  vibra-  -VIBRATION  OF 
tionsofthefork. 

Partly  fill  a  glass  goblet  with  water,  and  produce  a  musical  note  by 
drawing  a  bow  across  its  edge.  The  tremors  of  the  glass  will  throw 
the  surface  of  the  water  into  violent  agitation  in  four  sectors,  with 
intermediate  regions  of  relative  repose.  This  agitation  disappears 
when  the  sound  ceases. 


182  SOUND 

A  glass  tube,  four  or  five  feet  long,  may  be  made  to  emit  a  musical 
sound  by  .grasping  it  by  the  middle  and  briskly  rubbing  one  end  with 
a  cloth  moistened  with  water.  The  vibrations  are  longitudinal,  and 
may  be  so  energetic  as  to  break  the  tube  into  many  narrow  rings. 

Experiments  like  these  show  that  the  sources  of  sound 
are  bodies  in  a  state  of  vibration.  Sound  and  vibratory 
movement  are  so  related  that  one  is  strong  when  the  other 
is  strong,  and  they  diminish  and  cease  together. 

200.  Media  for  Transmitting  Sound.  —  Suspend  a  small  electric 
bell  in  a  bell  jar  on  the  air  pump  table  (Fig.  180).     When  the  air 

is  exhausted,  the  bell  is  nearly  inau- 
dible. Sound  does  not  travel  through 
a  vacuum. 

Fasten  the  stem  of  a  tuning  fork  to 
the  middle  of  a  thin  disk  of  wood. 
Set  the  fork  vibrating,  and  hold  it  with 
the  disk  resting  on  the  surface  of  water 
in  a  tumbler,  standing  on  a  table. 

The  sound,  which  is  scarcely  audible 
FIGURE  180.  — BELL  IN  VACUUM.  .  ...  . J  .  J 

when  there  is  no  disk  attached  to  the 

fork,  is  now  distinctly  heard  as  if  coming  from  the  table. 

Hold  one  end  of  a  long,  slender  wooden  rod  against  a  door,  and  rest 
the  stem  of  a  vibrating  fork  against  the  other  end.  The  sound  will  be 
greatly  intensified,  and  will  come  from  the  door  as  the  apparent  source. 

Press  down  on  a  table  a  handful  of  putty  or  dough,  and  insert  in  it 
the  stem  of  a  vibrating  fork ;  the  vibrations  will  not  be  conveyed  to 
the  table  to  an  appreciable  extent. 

Only  elastic  matter  transmits  sound,  and  some  kinds 
transmit  it  better  than  others. 

201.  Transmission  of  Sound  to  the  Ear.  —  Any   uninter- 
rupted series  of  elastic  bodies  will  transmit  sound  to  the 
ear,  be  they  solid,  liquid,  or  gaseous. 

A  bell  struck  under  water  sounds  painfully  loud  if  the  ear  of  the 
listener  is  also  under  water.  A  diver  under  water  can  hear  voices  in 
the  air.  By  placing  the  ear  against  the  steel  rail  of  a  railway,  two 
sounds  may  be  heard,  if  the  rail  is  struck  some  distance  away:  a 


Lord  Rayleigh  (John  William  Strutt)  was  born  at  Essex  in 
1842,  and  graduated  from  Cambridge  University  in  1865.  In 
1884  he  was  appointed  professor  of  experimental  physics  in  that 
institution,  and  three  years  later  he  was  elected  professor  of  natu- 
ral philosophy  at  the  Royal  Institution  of  Great  Britain.  His  work 
is  remarkable  for  its  extreme  accuracy.  The  discovery  of  argon 
in  the  atmosphere,  while  attempting  to  determine  the  density  of 
nitrogen,  was  the  result  of  a  very  minute  difference  between  the 
result  obtained  by  using  nitrogen  from  the  air  and  that  from 
another  source.  Nearly  every  department  of  physics  has  been 
enriched  by  his  genius.  His  treatise  on  Sound  is  one  of  the  finest 
pieces  of  scientific  writing  ever  produced.  His  determination  of 
the  electrochemical  equivalent  of  silver  and  the  electromotive 
force  of  the  Clark  standard  cell  are  important  contributions  to 
modern  electrical  measurements.  He  died  in  1919. 


Photographs  of  Sound- Waves  produced  by  an  Electric  Spark  behind  a 

Black  Disk. 

(Taken  by  Professor  Foley  of  Indiana  University.) 


1.  A  spherical  sound-wave. 

2.  The  same  wave  a  fraction  of  a  second  later. 

3.  Spherical  sound-wave  reflected  from  a  plate  of  plane  glass. 

4.  The  same  wave  a  moment  later.     The  broken  line  near  the  black  disk 

shows  the  effect  of  the  puff  of  hot  air  from  the  spark. 

5.  Sound-wave  reflected  from  a  parabolic  reflector.     The  source  is  at  the 

focus  and  the  reflected  wave  is  plane. 

6.  The  same  wave  a  moment  later,  showing  its  central  portion  advanced 

by  the  puff  of  hot  air  from  the  spark. 


MOTION   OF  THE  PARTICLES   OF  A    WAVE        183 

louder  one  through  the  rails  and  then  another  through  the  air.  The 
faint  scratching  of  a  pin  on  the  end  of  a  long  stick  of  timber,  or  the 
ticking  of  a  watch  held  against  it,  may  be  heard  very  distinctly  if  the 
ear  is  applied  to  the  other  end. 

The  earth  conducts  sound  so  well  that  the  stepping  of  a  horse  may 
be  heard  by  applying  the  ear  to  the  ground.  This  is  understood  by 
the  Indians.  The  firing  of  a  cannon  at  least  200  miles  away  may  be 
heard  in  the  same  way.  The  report  of  a  mine  blast  reaches  a  listener 
sooner  through  the  earth  than  through  the  air. 

The  great  eruption  of  Krakatoa  in  1883  gave  rise  to  gigantic 
sound  waves,  which  produced  at  a  distance  of  2000  miles  a  report 
like  the  firing  of  heavy  guns. 

202.  Sound  Waves.  —  When   a   tuning   fork   or   similar 
body  is  set  vibrating,  the  disturbances  produced  in  the 
air  about  it  are  known  as  sound  waves.     They  consist  of  a 
series  of  condensations  and  rarefactions  succeeding  each 
other  at  regular  intervals.     Each  particle  of  air  vibrates 
in  a  short  path  in  the  direction  of  the  sound  transmission. 
Its  vibrations  are  longitudinal  as  distinguished  from  the 
transverse  vibrations  in  water  waves. 

203.  Motion  of  the  Particles  of  a  Wave.  —  The  motion  of 
the  particles  of  the  medium  conveying  sound  is  distinct 
from  the  motion  of  the  sound  wave.     A  sound  wave  is 
composed  of  a   condensation  followed   by  a  rarefaction. 
In  the  former  the  particles  have  a  forward  motion  in  the 
direction  in  which  the  sound  is  traveling ;    in  the  latter 
they  have  a  backward  motion,  while  at  the  same  time  both 
condensation  and  rarefaction  travel  steadily  forward. 

The  independence  of  the  two  motions  is  aptly  illustrated  by  a  field  of 
grain  across  which  waves  excited  by  the  wind  are  coursing.  Each  stalk 
of  grain  is  securely  anchored  to  the  ground,  while  the  wave  sweeps 
onward.  The  heads  of  grain  in  front  of  the  crest  are  rising,  while  all 
those  behind  the  crest  and  extending  to  the  bottom  of  the  trough  are 
falling.  They  all  sweep  forward  and  backward,  not  simultaneously, 
but  in  succession,  while  the  wave  itself  travels  continuously  forward. 


184 


SOUND 
III.    VELOCITY  OF  SOUND 


204.  Velocity  in  Air.  —  In  1822  a  scientific  commission 
in  France  made  experiments  to  ascertain  the  velocity  of 
sound  in  air.  Their  method  was  to  divide  into  two  par- 
ties at  stations  a  measured  distance  apart,  and  to  determine 
the  interval  between  the  observed  flash  and  the  report  of 


VIEW  OF  LAKE  GENEVA. 

a  cannon  fired  alternately  at  the  two  stations.  The  mean 
of  an  even  number  of  measurements  eliminated  very  nearly 
the  effect  of  the  wind.  The  final  result  was  331  m.  per 
second  at  0°  C.  The  defect  of  the  method  is  that  the  per- 
ception of  sound  and  of  light  are  not  equally  quick,  and 
they  vary  with  different  persons. 

Subsequent  observers,  employing  improved  methods, 
and  correcting  for  all  sources  of  error,  have  obtained  as 
the  most  probable  velocity  332.4  m.,  or  1090.5  ft.,  per 
second  at  0°  C.  At  higher  temperatures  sound  travels 


QUESTIONS  AND  PROBLEMS  185 

faster,  the  correction  being  0.6  m.,  or  nearly  2  ft.,  per  de- 
gree Centigrade.  At  20°  C.  (68°  F.)  the  velocity  is  very 
nearly  1130  ft.  per  second. 

205.  Velocity  in  Water.  —  In  1827  Colladon  and  Sturm, 
'by  a  series  of  measurements  in  Lake  Geneva,  found  that 
sound  travels  in  water  at  the  rate  of  1435  m.  per  second  at 
a   mean   temperature   of   8.1°   C.     They  measured   with 
much  care  the  time  required  for  the  sound  of  a  bell  struck 
under  water  to  travel  through  the  lake  between  two  boats 
anchored  at  a  distance  apart  of  13,487  m.     It  was  9.4  sec- 
onds. 

A  system  of  transmitting  signals  through  water  by  means  of  sub- 
merged bells  is  in  use  by  vessels  at  sea  and  for  offshore  stations.  Spe- 
cial telephone  receivers  have  been  devised  to  operate  under  water  and 
to  respond  to  these  sound  signals.  Indeed,  the  vessel  itself  acts  as  a 
sounding  board  and  as  a  very  good  receiver. 

206.  Velocity  in  Solids.  —  The  velocity  of  sound  in  solids 
is  in  general  greater  than  in  liquids  on  account  of  their 
high  elasticity  as  compared  with  their  density.     The  ve- 
locity in  iron  is  5127  m.  per  second ;    in  glass  5026  m.  per 
second  ;  but  in  lead  it  is  only  1228  m.  per  second,  at  a 
temperature  in  each  case  of  0°  C. 

Questions  and  Problems 

1.  Why  do  the  timers  in  a  200-yd.  dash  start  their  stopwatches  by 
the  flash  of  the  pistol  rather  than  by  the  report  ? 

2.  If  the  flash  of  a  gun  is  seen  3, sec.  before  the  report  is  heard, 
how  far  is  the  gun  from  the  observer,  the  temperature  being  20°  C.  ? 

3.  The  interval  between  seeing  a  flash  of  lightning  and  hearing 
the  thunder  was  5  sec. ;  the  temperature  was  25°  C.     How  far  away 
was  the  lightning  discharge  ? 

4.  Signals  given  by  a  gun  2  mi.  away  would  be  how  much  in 
error  when  the  temperature  is  20°  C.  and  the  wind  is  blowing  10  mi. 
an  hour  in  the  direction  from  the  listener  to  the  gun  ? 


186  '    SOUND 

5.  A  man  sets  his  watch  by  a  steam  whistle  which  blows  at  12 
o'clock.     The  whistle  is  1.5  mi.  away  and  the   temperature '  15°  C. 
How  many  seconds  will  the  watch  be  in  error? 

6.  A  ball  fired  at  a  target  was  heard  to  strike  after  an  interval  of 
8  sec.     The  distance  of  the  target  was  1  mi.  and  the  temperature  of 
the  air  20°  C.     What  was  the  mean  velocity  of  the  ball  ? 

7.  The  distance  between  two  points  on  a  straight  stretch  of  rail- 
way is  2565  m.     An  observer  listens  at  one  of  these  points  and  a 
blow  is  struck  on  the  rails  at  the  other.     If  the  temperature  is  0°  C., 
what  is  the  interval  between   the   arrival  of   the  two   sounds,  one 
through  the  rails  and  the  other  through  the  air? 

8.  A  man  watching  for  the  report  of  a  signal  gun  saw  the  flash 
2  sec.  before  he  heard  the  report.     If  the  temperature  was  0°  C.  and 
the  distance  of  the  signal  gun  was  2225  ft.,  what  was  the  velocity  of 
the  wind  ? 

9.  A  shell  fired  at  a  target,  distance  half  a  mile,  was  heard  to 
strike  it  5  sec.  after  leaving  the  gun.     What  was  the  average  speed 
of  the  bullet,  the  temperature  of  the  air  being  20°  C.  ? 

IV.    REFLECTION  OF  SOUND 

207.  Echoes.  —  An  echo  is  the  repetition  of  a  sound  by  re- 
flection from  some  distant  surface.  A  clear  echo  requires 
a  vertical  reflecting  surface,  the  dimensions  of  which  are 
large  compared  to  the  wave  length  of  the  sound.  A  cliff, 
a  wooded  hill,  or  the  broad  side  of  a  large  building  may 
serve 'as  the  reflecting  surface.  Its  inequalities  must  be 
small  compared  to  the  length  of  the  incident  sound  waves  ; 
otherwise,  the  sound  is  diffused  in  all  directions. 

A  loud  sound  in  front  of  a  tall  cliff  an  eighth  of  a  mile 
away  will  be  returned  distinctly  after  about  a  second  and 
a  sixth.  If  the  reflecting  surface  is  nearer  than  about  fifty 
feet,  the  reflected  sound  tends  to  strengthen  the  original 
one,  as  illustrated  by  the  greater  distinctness  of  sounds 
indoors  than  in  the  open  air.  In  large  rooms  where  the 
echoes  produce  a  confusion  of  sounds  the  trouble  may  be 


I 


I 


2      £ 
b)        O 

It 


AERIAL  ECHOES 


187 


diminished  by  adopting  some  method  to  prevent  regular 
reflection,  such  as  the  hanging  of  draperies,  or  covering 
the  walls  with  absorbing  materials. 

208.  Multiple  Echoes.  —  Parallel  reflecting  surfaces  at  a 
suitable  distance  produce  multiple  echoes,  as  parallel  mir- 
rors   produce    multiple 

images  (§  261).  The 
circular  baptistery  at 
Pisa  and  its  spherical 
dome  prolong  a  sound 
for  ten  or  more  seconds 
by  successive  reflec- 
tions; the  effect  is  made 
more  conspicuous  by  the 
good  reflecting  surface 
of  polished  marble.  Ex- 
traordinary echoes  some- 
times occur  between  the 
parallel  walls  of  deep 
canons. 

209.  Aerial  Echoes.— 
Whenever  the  medium 

transmitting  sound  changes  suddenly  in  density,  a  part  of 
the  energy  is  transmitted  and  a  part  reflected.  The  in- 
tensity of  the  reflected  system  is  the  greater  the  greater 
the  difference  in  the  densities  of  the  two  media.  A  dry 
sail  reflects  a  part  of  the  sound  and  transmits  a  part ; 
when  wet  it  becomes  a  better  reflector  and  is  almost  im- 
pervious to  sound. 

Aerial  echoes  are  accounted  for  by  sudden  changes  of 
density  in  the  air.  Air,  almost  perfectly  transparent  to 
light,  may  be  very  opaque  to  sound.  When  for  any  rea- 
son the  atmosphere  becomes  unstable,  vertical  currents 


THE  BAPTISTERY  AT  PISA. 


188  SOUND 

and  vertical  banks  of  air  of  different  densities  are  formed. 
The  sound  transmitted  by  one  bank  is  in  part  reflected  by 
the  next,  the  successive  reflections  giving  rise  to  a  curious 
prolonging  of  a  short  sound.  Thus,  the  sound  of  a  gun 
or  of  a  whistle  is  then  heard  apparently  rolling  away  to  a 
great  distance  with  decreasing  loudness. 

210.  Whispering  Gallery.  —  Let  a  watch  be  hung  a  few  inches 
in  front  of  a  large  concave  reflector  (Fig.  181).     A  place  may  be  found 

for  the  ear  at  some  distance  in 
front,  as  at  E,  where  the  ticking  of 
the  watch  may  be  heard  with  great 
distinctness.  The  sound  waves, 
after  reflection  from  the  concave 
surface,  converge  to  a  point  at  E. 

The  action  of   the  ear  trumpet 
FIGURE  181.  —  REFLECTOR    FOR     ••          -,          ,,         a     ,.         ,.  j 

_  depends  on  the  reflection  of  sound 

from  curved  surfaces;   the  sides  of 

the  bell-shaped  mouth  reflect  the  sound  into  the  tube  which  conveys 
it  to  the  ear. 

An  interesting  case  of  the  reflection  of  sound  occurs  in 
the  whispering  gallery,  where  a  faint  sound  produced  at 
one  point  of  a  very  large  room  is  distinctly  heard  at  some 
distant  point,  but  is  inaudible  at  points  between.  It  re- 
quires curved  walls  which  act  as  reflectors  to  concentrate 
the  waves  at  a  point.  Low  whispers  on  one  side  of  the 
dome  of  St.  Paul's  in  London  (see  page  81)  are  distinctly 
audible  on  the  opposite  side. 

V.    RESONANCE 

211.  Forced  Vibrations.  — A  body  is  often  compelled  to 
surrender  its  natural  period  of  vibration,  and  to  vibrate 
with  more  or  less  accuracy  in  a  manner  imposed  on  it  by 
an  external  periodic  force.     Its  vibrations  are  then  said 
to  be  forced. 


SYMPATHETIC  VIBRATIONS  189 

Huyghens  discovered  that  two  clocks,  adjusted  to  slightly  differ' 
ent  rates,  kept  time  together  when  they  stood  on  the  same  shelf. 
The  two  prongs  of  a  tuning  fork,  with  slightly  different  natural 
periods  on  account  of  unavoidable  differences,  mutually  compel  each 
other  to  adopt  a  common  frequency.  These  two  cases  are  examples 
of  mutual  control,  and  the  vibrations  of  both  members  of  each  pair 
are  forced. 

The  sounding  board  of  a  piano  and  the  membrane  of  a  banjo  are 
forced  into  vibration  by  the  strings  stretched  over  them.  The  top 
of  a  wooden  table  may  be  forced  into  vibration  by  pressing  against 
it  the  stem  of  a  vibrating  tuning  fork.  The  vibrations  of  the  table 
are  forced  and  it  will  respond  to  a  fork  of  any  period. 

212.  Sympathetic  Vibrations.  —  Place  two  mounted  tuning 
forks,  tuned  to  exact  unison,  near  each  other  on  a  table.  Keep  one 
of  them  in  vibration  for  a  few  seconds  and  then  stop  it;  the  other 
one  will  be  heard  to  sound. 

In  the  case  of  these  forks,  the  pulses  in  the  air  reafch 
the  second  fork  at  intervals  corresponding  to  its  natural 
vibration  period  and  the  effect  is  cumulative.  The  ex- 
periment illustrates  sympathetic  vibrations  in  bodies  hav- 
ing the  same  natural  period.  If  the  forks  differ  in  period, 
the  impulses  from  the  first  do  not  produce  cumulative 
effects  on  the  second,  and  it  will  fail  to  respond. 

Suspend  a  heavy  weight  by  a  rope  and  tie  to  it  a  thread.  The 
weight  may  be  set  swinging  by  pulling  gently  on  the  thread,  releas- 
ing it,  and  pulling  again  repeatedly  when  the  weight  is  moving  in 
the  direction  of  the  pull. 

Suspend  two  heavy  pendulums  on  knife-edges  on  the  same  stand, 
and  carefully  adjust  them  to  swing  in  the  same  period.  If  then  one 
is  set  swinging,  it  will  cause  the  other  one  to  swing,  and  will  give  up 
to  it  nearly  all  its  own  motion. 

When  the  wires  of  a  piano  are  released  by  pressing  the  loud  pedal, 
a  note  sung  near  it  will  be  echoed  by  the  wire  which  gives  a  tone  of 
the  same  pitch. 

A  number  of  years  ago  a  suspension  bridge  of  Manchester  in  Eng- 
land was  destroyed  by  its  vibrations  reaching  an  amplitude  beyond 


190 


SOUND 


•—•IP  css^3\ 
^Bi      ^^^PII 


the  limit  of  safety.     The  cause  was  the  regular  tread  of  troops  keep- 
ing time  with  what  proved  to  be  the  natural  rate  of  vibration  of  the 

bridge.     Since  then  the  custom  has 
always  been  observed  of  breaking 
step  when  bodies  of  troops  cross  a 
^    bridge. 

213.  Resonance.  —  Reso- 
nance is  the  reenf or  cement  of 
sound  by  the  union  of  direct 
and  reflected  sound  waves. 

Hold  a  vibrating  tuning  fork 
over  the  mouth  of  a  cylindrical  jar 
(Fig.  182).  ,  Change  the  length  of 
the  air  column  by  pouring  in  water 
slowly.  The  sound  will  increase  in 
loudness  until  a  certain  length  is 
reached,  after  which  it  becomes 
weaker.  A  fork  of  different  pitch 
OF  will  require  a  different  length  of 

air  column  to  reenforce  its  sound. 
The  " sound  of  the  sea"  heard  when  a  sea  shell  is  held  to  the  ear 

is  a  case  of  resonance.     The  mass  of  air  in  the  shell  has  a  vibration 

rate  of  its  own,  and  it  amplifies  any 

faint  sound  of  the  same  period.     A 

vase  with  a  long  neck,  or  even  a  tea- 
cup, will  also  exhibit  resonance. 
The  box  on  which  a  tuning  fork 

is  mounted  (Fig.  183)  is  a  resonator, 

designed  to  increase  the  volume  of 

sound.     The  air  within  the  body  of 

a  violin  and  all  instruments  of  like 

character  acts  as  a  resonator.     The 

air  in  the  mouth,   the  larynx,   and 

the  nasal  passages  is  a  resonator ;  the 


-'•- 


FIGURE  182. 


—  REENFORCEMENT 
SOUND. 


FIGURE  183. —  MOUNTED   TUNING 
length  and  volume  of  this  body  of  air  FORK. 

can  be  changed  at  pleasure  so  as  to  reenforce  sounds  of  different 
pitch. 


PITCH 


191 


214.  The  Helmholtz  Resonator.  —  The  resonator  devised  by 
Helmholtz   is  spherical  in  form,  with  two  short  tubes  on  opposite 
sides     (Fig.    184).     The    larger 

opening  A  is  the  mouth  of  the 
resonator ;  the  smaller  one  B  fits 
in  the  ear.  These  resonators  are 
made  of  thin  brass  or  of  glass, 
and  their  pitch  is  determined  by 
their  size.  When  one  of  them 
is  held  to  the  ear,  it  strongly 
reenforces  any  sound  of  its  own 
rate  of  vibration,  but  is  silent  to 
others.  FIGURE  1 84.  —  HELMHOLTZ  RESONATOR. 

VI.   CHARACTERISTICS  OF  MUSICAL  SOUNDS 

215.  Musical  Sounds.  —  Sounds  are   said   to  be   musical 
when  they  are  pleasant  to  the  ear.     They  are  caused  by 
regular   periodic   vibrations.     A   noise   is  a  disagreeable 
sound,  either  because  the  vibrations  producing  it  are  not 

periodic,  or  because  it  is  a  mixture  of  dis- 
cordant elements,  like  the  clapping  of  the 
hands. 

Musical  sounds  have  three  distinguish- 
ing characteristics :  pitch,  loudness,  and 
quality. 


216.  Fitch.  —  Mount  on  the  axle  of  a  whirling 
machine  (Fig.  185),  or  on  the  armature  of  a  small 
electric  motor,  a  cardboard  or  metal  disk  D  with 
a  series  of  equidistant  holes  in  a  circle  near  its 
edge.  While  the  disk  is  rotating  rapidly,  blow  a 
stream  of  air  through  a  small  tube  against  the 
circle  of  holes.  A  distinct  musical  tone  will  be 
produced.  If  the  experiment  be  repeated  with  the 
disk  rotating  more  slowly,  or  with  a  circle  of  a 

smaller  number  of  holes,  the  tone  will  be  lower;  if  the  disk  is  rotated 

more  rapidly,  the  tone  will  be  higher. 


FIGURE    185.  — 
SIREN. 


192  SOUND 

The  air  passes  through  the  holes  in  a  succession  of  puffs  producing 
waves  in  the  air.  These  waves  follow  one  another  with  definite 
rapidity,  giving  rise  to  the  characteristic  of  sound  called  pitch.  We 
conclude  that  the  pitch  of  a  musical  sound  depends  only  upon  the  number 
of  pulses  which  reach  the  ear  per  second.  To  Galileo  belongs  the  credit 
of  first  pointing  out  the  relation  of  pitch  to  frequency  of  vibration. 
He  illustrated  it  by  drawing  the  edge  of  a  card  over  ths  milled  edge 
of  a  coin. 

217.  Relation  between  Pitch,  Wave  Length,  and  Velocity. — 
If  a  tuning  fork  makes  256  vibrations  per  second,  and 
in  that  time  a  sound  travels  in  air,  at  20°  C.,  a  distance  of 
344m.,  then  the  first  wave  will  be  344m.  from  the  fork 
when  it  completes  its  256th  vibration.  Hence,  in  344  m., 
there  will  be  256  waves,  and  the  length  of  each  will  be 
m.,  or  1.344  m.  In  general,  then, 


wave  length  =    velocitV  , 
frequency 

or  in  symbols,  I  =  -,  v  =  nl,  and  n  —  -.     .     (Equation  31) 
n  I 

218.  Loudness.  —  The  loudness  of  a  sound  depends  on 
the  intensity  of  the  vibrations  transmitted  to  the  ear. 
The  energy  of  the  vibrations  is  proportional  to  the  square 
of  their  amplitude  ;  but  since  it  is  obviously  impracticable 
to  express  a  sensation  in  terms  of  a  mathematical  formula, 
it  is  sufficient  to  say  that  the  loudness  of  a  sound  increases 
with  the  amplitude  of  vibration. 

As  regards  distance,  geometrical  considerations  would 
go  to  show  that  the  energy  of  sound  waves  in  the  open 
decreases  as  the  square  of  the  distance  increases,  but  the 
actual  decrease  in  the  intensity  of  sound  is  even  greater 
than  this.  The  energy  of  sound  waves  is  gradually  dis- 
sipated by  conversion  into  heat  through  friction  and 
viscosity. 


Hermann  von  Helmholtz  (1821-1894)  was  born  at  Potsdam. 
He  received  a  medical  education  at  Berlin  and  planned  to  be  a 
specialist  in  diseases  of  the  eye,  ear,  and  throat.  His  studies  soon 
revealed  to  him  the  need  of  a  knowledge  of  physics  and  mathe- 
matics. To  these  subjects  he  gave  his  earnest  attention  and  soon 
became  one  of  the  greatest  physicists  and  mathematicians  of  the 
nineteenth  century.  He  made  important  contributions  to-  all  de- 
partments of  physical  science.  He  is  the  author  of  an  important 
work  on  acoustics  and  is  celebrated  for  his  discoveries  in  this 
field.  But  perhaps  his  most  useful  contribution  is  that  of  the 
ophthalmoscope,  an  instrument  of  inestimable  value  to  the  oculist 
in  examining  the  interior  of  the  eye. 


QUALITY  193 

The  area  of  the  vibrating  body  affects  the  loudness. 
This  is  illustrated  in  the  piano,  where  strings  of  different 
diameters  produce  sounds  differing  in  loudness.  The 
thicker  vibrating  string  sets  more  air  in  motion,  and  the 
wave  has  in  consequence  more  energy. 

The  less  dense  the.  medium  in  which  the  vibration  is  set 
up,  the  feebler  the  sound.  On  a  mountain  top  the  report 
of  a  gun  is  comparable  in  loudness  with  that  produced  by 
the  breaking  of  a  stick  at  the  base.  The  electric  bell  in  a 
partially  exhausted  receiver  (§  200)  is  nearly  inaudible. 

Fill  three  large  battery  jars  with  coal  gas,  air,  and  carbonic  acid 
respectively.  Ring  in  them  successively  a  small  bell.  There  will  be 
a  marked  difference  in  loudness. 

219.  Quality. — Two  notes  of  the  same  pitch  and  loud- 
ness,  such  as  those  of  a  piano  and  a  violin,  are  yet  clearly 
distinguishable  by  the  ear.  This  distinction  is  expressed 
by  the  term  quality  or  timbre.  Helmholtz  demonstrated 
that  the  quality  of  a  note  is  determined  by  the  presence  of 
tones  of  higher  pitch,  whose  frequencies  are  simple  mul- 
tiples of  that  of  the  fundamental  or  lowest  tone.  These 
are  known  as  overtones. 

The  quality  of  sounds  differs  because  of  the  series  of 
overtones  present  in  each  case.  Voices  differ  for  this 
reason.  Violins  differ  in  sweetness  of  tone  because  the 
sounding  boards  of  some  bring  out  overtones  different 
from  those  of  others.  Even  the  untrained  ear  can  readily 
appreciate  differences  in  the  character  of  the  music  pro- 
duced by  a  flute  and  a  cornet.  Voice  culture  consists  in 
training  and  developing  the  vocal  organs  and  resonance 
cavities,  to  the  end  that  purer  overtones  may  be  secured, 
and  greater  richness  may  by  this  means  be  imparted  to 
the  voice. 


194 


SOUND 


VII.   INTERFERENCE  AND  BEATS 

220.    Interference.  —  Hold  a  vibrating  tuning  fork  over  a  cylin- 
drical jar  adjusted  as  a  resonator,  and  turn  the  fork  on  its  axis  until 

a  position  of  minimum 
loudness  is  found.  In  this 
position  cover  one  prong 
with  a  pasteboard  tube 
without  touching  (Fig. 
186).  The  sound  will  be 
restored  to  nearly  maxi- 
mum loudness,  because 
the  paper  cylinder  cuts  off 
the  set  of  waves  from  the 
covered  prong. 

It  is  well  known 
that  the  loudness  of 
the  sound  of  a  vibrat- 
ing fork  held  freely 
in  the  hand  near  the 
ear,  and  turned  on  its 
stem,  exhibits  marked  variations.  In  four  positions  the 
sound  is  nearly  inaudible.  Let  A,  B  (Fig.  187)  be  the 
ends  of  the  two  prongs.  They  vibrate  with  the  same  fre- 
quency, but  in  opposite  direc- 
tions, as  indicated  by  the  arrows.  \ 
When  the  two  approach  each 
other,  a  condensation  is  pro- 
duced between  them,  and  at  the 
same  time  rarefactions  start 
from  the  backs  at  c  and  d.  The 
condensations  and  rarefactions 
meet  along  the  dotted  lines  of  /'  \ 

equilibrium,  where  partial  ex-    'FIQURE  187._lNTERPERENOEN 
tinction  occurs,  because  a  rare-     FROM  PRONGS  OF  TUNING  FORK. 


FIGURE  186.  —  INTERFERENCE. 


\ 


BEATS 


195 


faction  nearly  annuls  a  condensation.  When  the  fork  is 
held  over  the  resonance  jar  so  that  one  of  these  lines  of 
interference  runs  into  the  jar,  the  paper  cylinder  cuts  off 
one  set  of  waves,  and  leaves  the  other  to  be  reenforced  by 
the  air  in  the  jar. 

Interference  is  the  superposition  of  two  similar  sets  of 
waves  traversing  the  medium  at  the  same  time.  One  of 
the  two  sets  of  similar  waves  may  be  direct  and  the  other 
reflected.  If  two  sets  of  sound  waves  of  equal  length  and 
amplitude  meet  in  opposite  phases,  the  condensation  of  one 
corresponding  with  the  rarefaction  of  the  other,  the  sound 
at  the  place  of  meeting  is  extinguished  by  interference. 

221.  Beats.  —  Place  near  each  other  two  large  tuning  forks  of 
the  same  pitch  and  mounted  on  resonance  boxes.  When  both  are  set 
vibrating,  the  sound  is  smooth,  as  if  only  one  fork  were  sounding. 
Stick  a  small  piece *of  wax  to  a  prong  of  one  fork:  this  load  increases 
its  periodic  time  of  vibration,  and 
the  sound  given  by  the  two  is  now 
pulsating  or  throbbing. 

Mount  two  organ  pipes  of  the  same 
pitch  on  a  bellows,  and  sound  them 
together.  If  they  are  open  pipes,  a 
card  gradually  slipped  over  the  open 
end  of  one  of  them  will  change  its 
pitch  enough  to  bring  out  strong 
pulsations. 

With  glass  tubes  and  jet  tubes  set 
up  the  apparatus  of  Fig.  188.  One 
tube  is  fitted  with  a  paper  slider  so 
that  its  length  may  be  varied.  When 
the  gas  flame  is  turned  down  to  the 
proper  size,  the  tube  gives  a  continu- 
ous sound  known  as  a  "singing 
flame."  By  making  the  tubes  the 
same  length,  they  may  be  made  to  yield  the  same  note,  the  com- 
bined sound  being  smooth  and  steady.  Now  change  the  position 


FIGURE  188.  —  INTERFERENCE  WITH 
SINGING  FLAMES. 


196  SOUND 

of  the  slider,  and  the  sound  will  throb  and  pulsate  in  a  disagreeable 
manner. 

These  experiments  illustrate  the  interference  of  two  sets 
of  sound  waves  of  slightly  different  period.  The  outbursts 
of  sound,  followed  by  short  intervals  of  comparative  silence, 
are  called  beats. 

Figure  189  illustrates  the  composition  of  two  transverse 
waves  of  slightly  different  length.  The  addition  of  the 


FIGURE  189.  —  INTERFERENCE  OF  Two  TRANSVERSE  WAVES. 

ordinates  of  the  two  waves  ABO  gives  the  wave  A' B'C', 
with  a  minimum  amplitude  at  B* . 

222.  Number  of  Beats.  —  If  two  sounds  are  produced  by 
forks,  for  example,  making  100  and   110  vibrations  per 
second  respectively,  then  in  each  second  the  latter  fork 
gains  ten  vibrations  on  the  former.     There  must  be  ten 
times  during  each  second  when  they  are  vibrating  in  the 
same  phase,  and  ten  times  in  opposite  phase.     Hence,  in- 
terference of  sound  must  occur  ten  times  a  second,  and 
ten  beats  are  produced.     Therefore,  the  number  of  beats 
per  second  is  equal  to  the  difference  of  the  vibration  rates 
(frequencies)  of  the  two  sounds. 

VIII.    MUSICAL  SCALES 

223.  Musical  Intervals.  —  A  musical  interval  is  the  rela- 
tion  between  two  notes  expressed  as  the  ratio  of  their 
frequencies  of  vibration.     Many  of  these  intervals  have 


THE  MAJOR  DIATONIC  SCALE 


197 


names  in  music.  When  the  ratio  is  1,  the  interval  is 
called  unison  ;  2,  an  octave  ;  |,  a  fifth  ;  %,  a  fourth  ;  etc. 
Any  three  notes  whose  frequencies  are  as  4:5:6  form  a 
major  triad,  and  alone  or  together  with  the  octave  of  the 
lowest  note,  a  major  chord.  Any  three  notes  whose  fre- 
quencies are  as  10  :  12:  15  form  a  minor  triad,  and  alone  or 
with  the  octave  of  the  lowest,  a  minor  chord. 

Mount  the  disk  of  Fig.  190  on  the  whirling  table  of  Fig.  185.  The 
disk  is  perforated  with  four  circles  of  equidistant  holes,  numbering 
24,  30,  36,  and  48  respectively.  These  are 
in  the  relation  of  4,  5,  6,  8.  Rotate  with 
uniform  speed,  and  beginning  with  the 
inner  circle,  blow  a  stream  of  air  against 
each  row  of  holes  in  succession.  The 
tones  produced  will  be  recognized  as  do, 
mi,  sol,  do',  forming  a  major  chord.  If 
now  the  speed  of  rotation  be  increased, 
each  note  will  rise  in  pitch,  but  the  musical 
sequence  will  remain  the  same. 


FlGURE  190.  —  DISK  FOR 
MAJOR  CHORD. 


It  will  be  seen  from  the  fore- 
going relations  that  harmonious 
musical  intervals  consist  of  very  simple  vibration  ratios. 

224.  The  Major  Diatonic  Scale.  —  A  musical  scale  is  a 
succession  of  notes  by  which  musical  composition  ascends 
from  one  note,  called  the  keynote,  to  its  octave.  This  last 
note  in  one  scale  is  regarded  as  the  keynote  of  another 
series  of  eight  notes  with  the  same  succession  of  intervals. 
In  this  way  the  series  is  extended  until  the  limit  of  pitch 
established  in  music  is  reached. 

The  common  succession  of  eight  notes,  called  the  major 
diatonic  scale,  was  adopted  about  three  hundred  and  fifty 
years  ago.  The  octave  beginning  with  middle  0  is  written 

<?'      d'     e'    f     g'      a'      V      c" 


198  SOUND 

The  three  major  triads  for  the  keynote  of  0  are : 

*'    :    e>    :    /  1 

g'    :    &    :    d"[::4:5:6 

/'    :    «'    :    *"J 

The  frequency  universally  assigned  to  c'  in  physics  is 
256.  It  is  convenient  because  it  is  a  power  of  2,  and  it 
is  practically  that  of  the  "middle  <7"  of  the  piano  If  c' 
is  due  to  256,  or  m,  vibrations  per  second,  the  frequency 
of  the  other  notes  of  the  diatonic  scale  may  be  found  by 
proportion  from  the  three  triads  above;  they  are  as 
follows : 

256  288  -320  341£  384  426f  480  512 

c1  d'  e'  f          g'           af  bf          c" 

do  re  mi  fa  sol         la  si          do 

m  f  m  4m  4m  \m  &  m  -^  m  2m 

O  t  o  A  o  o 

If  the  fractions  representing  the  relative  frequencies  be 
reduced  to  a  common  denominator,  the  numerators  may 
be  taken  to  denote  the  relative  frequencies  of  the  eight 
notes  of  the  scale.  They  are 

24     27     30     32     36     40     45    48 

An  examination  of  these  numbers  will  show  that  there 
are  only  three  intervals  from  any  note  to  the  next  higher. 
They  are  |,  a  major  tone ;  -ag°-,  a  minor  tone ;  and  if,  a 
half  tone.  The  order  is  f ,  J£,  If,  f ,  ^-,  f ,  if. 

225.  The  Tempered  Scale.  —  If  0  were  always  the  key- 
note, the  diatonic  scale  would  be  sufficient  for  all  purposes 
except  for  minor  chords  ;  but  if  some  other  note  be  chosen 
for  the  keynote,  in  order  to  maintain  the  same  order  of 
intervals,  new  and  intermediate  notes  will  have  to  be  in- 
troduced. For  example,  let  D  be  chosen  for  the  key- 


LIMITS  OF  PITCH  199 

note,  then  the  next  note  will  be  288  x  f  =  324  vibrations, 
a  number  differing  slightly  from  E.  Again,  324  x  *£- 
=  360,  a  note  differing  widely  from  any  note  in  the  series. 
In  like  manner,  if  other  notes  are  taken  as  keynotes,  and 
a  scale  is  built  up  with  the  order  of  intervals  of  the  dia- 
tonic scale,  many  more  new  notes  will  be  needed.  This 
interpolation  of  notes  for  both  the  major  and  minor  scales 
would  increase  the  number  in  the  octave  to  seventy-two. 

In  instruments  with  fixed  keys  such  a  number  is  un- 
manageable, and  it  becomes  necessary  to  reduce  the  num- 
ber by  changing  the  value  of  the  intervals.  Such  a  modi- 
fication of  the  notes  is  called  tempering.  Of  the  several 
methods  proposed  by  musicians,  that  of  equal  temperament 
is  the  one  generally  adopted.  It  makes  all  the  intervals 
from  note  to  note  equal,  interpolates  one  note  in  each 
whole  tone  of  the  diatonic  scale,  and  thus  reduces  the 
number  of  intervals  in 
the  octave  to  twelve.  BE 

IKS 

The    only    accurately    ^^ 

tuned  interval  in  this 

scale  is  the  octave  ;  all 

the  others  are  more  or 

less  modified.    The  fol  -  F]OURE  m  _  SCALE  op  c 

lowing  table  shows  the 

differences  between  the  diatonic  and  the  equally  tempered 

scales  : 

c'        d'          e'  f          gr          a'          V  c" 

Diatonic    .     .     .  256  288  320  341.3  384  426.7  480  512 

Tempered.     .    .256  287.3  322.5  341.7  383.6  430.5  483.3  512 

Figure  191  illustrates  the  scale  of  0  on  the  staff  and  the 
keyboard. 

226.  Limits  of  Pitch.  —  The  international  pitch,  now  in 
general  use  in  Europe  and  America,  assigns  to  ar  the  vi- 


•uTe'l/Tg"«T 


200  SOUND 

bration  frequency  of  435.  But  some  orchestras  have 
adopted  440  vibrations  for  a' '.  In  the  modern  piano  of 
seven  octaves  the  bass  A  has  a  frequency  of  about  27.5, 
the  highest  A,  3480.  The  lowest  note  of  the  organ  is  the 
O  of  16  vibrations  per  second ;  the  highest  note  is  the 
same  as  the  highest  note  of  the  piano,  the  third  octave 
above  a1 ',  with  a  frequency  of  3480. 

The  limits  of  hearing  far  exceed  those  of  music.  The 
range  of  audible  sounds  is  about  eleven  octaves,  or  from 
the  O  of  16  vibrations  to  that  of  32,768,  though  many 
persons  of  good  hearing  perceive  nothing  above  a  fre- 
quency of  16,384,  an  octave  lower. 

Questions  and  Problems 

1.  Why  is  the  pitch  of  the  sounds  given  by  a  phonograph  raised  by 
increasing  the  speed  of  the  cylinder  or  the  disk  containing  the  record? 

2.  A  megaphone  or  a  speaking  tube  makes  a  sound  louder  at  a 
distance.     Explain  why. 

3.  The  teeth  of  a  circular  saw  give  a  note  of  high  pitch  when 
they  first  strike  a  plank.     Why  does  the  pitch  fall  when  the  plank  is 
pushed  further  against  the  saw  ? 

4.  Miners  entombed  by  a  fall  of  rock  or  by  an  explosion  have 
signaled  by  taps  on  a  pipe  or  by  pounding  on  the  rock.     How  does 
the  sound  reach  the  surface  ? 

5.  Two  Rookwood  vases  in  the  form  of   pitchers  with  slender 
necks  give  musical  sounds  when  one  blows  across  their  mouth.     Why 
does  the  larger  one  give  a  note  of  lower  pitch  than  the  smaller? 

6.  What  note  is  made  by  three  times  as  many  vibrations  as  cf 
(middle  C)  ? 

7.  If  c'  is  due  to  256  vibrations  per  second,  what  is  the  frequency 
of  g"  in  the  next  octave  ? 

8.  What  is  the  wave  length  of  g'  when  sound  travels  1130  feet 
per  second? 

9.  If  c'  has  264  vibrations  per  second,  how  many  has  a'? 

10.  When  sound  travels  1120  ft.  per  second,  the  wave  length  of  the 
note  given  by  a  fork  was  3.5  ft.  What  was  the  pitch  of  the  fork  ? 


LAWS   OF  STRINGS  201 

IX.   VIBRATION  OF  STRINGS 

227.  Manner  of  Vibration.  —  When  strings  are  used  to 
produce  sound,  they  are  fastened  at  their  ends,  stretched 
to  the  proper  tension,  and  are  made  to  vibrate  transversely 
by  drawing  a  bow  across  them,  striking  with  a  light  ham- 
mer as  in  the  piano,  or  plucking  with  the  fingers  as  in  the 
banjo,  guitar,  or  harp. 

228.  The  Sonometer.  —  The  sonometer  is  an  instrument 
for   the   study    of   the   laws   governing  the  vibration  of 


FIGURE  192.  —  SONOMETER. 

strings.  It  consists  of  a  thin  wooden  box,  across  which  are 
stretched  violin  strings  or  thin  piano  wires  (Fig.  192). 
The  wires  pass  over  fixed  bridges,  A  and  B,  near  the  ends, 
and  are  stretched  by  tension  balances  at  one  end.  They 
may  be  shortened  by  movable  bridges  (7,  sliding  along 
scales  under  the  wires. 

229.  Laws  of  Strings..  —  Stretch  two  similar  wires  on  the  so- 
nometer and  tune  to  unison  by  varying  the  tension.  Shorten  one  of 
them  by  moving  the  bridge  C  to  f,  f ,  f ,  f ,  etc.  The  successive  inter- 
vals between  the  notes  given  by  the  two  wires  will  be  f,  f,  $,  f,  etc. 
The  notes  given  by  the  wire  of  variable  length  are  those  of  the  major 
diatonic  scale.  Hence, 

The  frequency  of  vibration  for  a  given  tension  varies 
inversely  as  the  length. 

Starting  with  a  given  tension  and  the  strings  or  wires  in  unison, 
increase  the  stretching  force  on  one  of  them  four  times ;  it  will  now 
give  the  octave  of  the  other  with  twice  the  frequency.  Increase  the 


202  SOUND 

tension  nine  times ;  it  will  give  the  octave  plus  the  fifth,  or  the  twelfth, 
above  the  other  with  three  times  the  frequency.  These  statements 
may  be  verified  by  dividing  the  comparison  wire  by  a  bridge  into 
halves  and  thirds,  so  as  to  put  it  in  unison  with  the  wire  of  variable 
tension.  Hence, 

When  the  length  is  constant,  the  frequency  varies  as 
the  square  root  of  the  tension. 

Stretch  equally  two  wires  differing  in  diameter  and  material,  that 
is,  in  mass  per  unit  length.  Bring  them  to  unison  with  the  movable 
bridge.  The  ratio  of  their  lengths  will  be  inversely  as  that  of  the 
square  roots  of  the  masses  per  unit  length.  Hence, 

The  length  and  tension  being  constant,  the  frequency 
varies  inversely  as  the  square  root  of  the  mass  per  unit 
length. 

230.  Applications.  —  In  the  piano,  violin,  harp,  and  other 
stringed  instruments,  the  pitch  of  each  string  is  determined 
partly  by  its  length,  partly  by  its  tension,  and  partly  by 
its  size  or  the  mass  of  fine  wire  wrapped  around  it.     The 
tuning  is  done  by  varying  the  tension. 

231.  Fundamental  Tone.  —  Fasten  one  end  of  a  silk  cord  about 
a  meter  long  to  one  prong  of  a  large  tuning  fork,  arid  wrap  the  other 

end  around  a  wooden  pin  in- 
serted in  an  upright  bar  in 
such  a  way  tha*  tension  can 
be  applied  to  the  cord  by 
turning  the  pin.  Set  the 
fork  vibrating,  and  adjust 

FIGURE  193.  — FUNDAMENTAL  OF  A  STRING,  the  tension  until  the  cord 

vibrates  as  a  whole  (Fig. 

193).     Arranged  in  this  way,  the  frequency  of  the  fork  is  double  that 

of  the  cord. 

The  experiment  shows  the  way  a  string  or  wire  vibrates 
when  giving  its  lowest  or  fundamental  tone.  A  body 


NODES  AND  SEGMENTS 


203 


yields  its  fundamental  tone  when  vibrating  as  a  whole,  or 
in  the  smallest  number  of  segments  possible 

232.  Nodes  and  Segments.  — With  a  silk  cord  about  2  m.  long, 
and  mounted  as  in  the  last  experiment,  adjust  the  tension  until  the 
cord  vibrates  in  a  number  of 
parts,  giving  the  appearance 
of  a  succession  of  spindles  of 
equal  length  (Fig.  194).  The 
frequency  of  the  fork  is  twice 
that  of  each  spindle. 

Stretch  a  wire  on  a  sonom- 
eter with  a  thin  slip  of  cork 
strung  on  it.  Place  the  cork  at  one  third,  one  fourth,  one  fifth,  or  one 
sixth  part  of  the  wire  from  one  end ;  touch  it  lightly,  and  bow  the 
shorter  portion  of  the  wire.  The  wire  will  vibrate  in  equal  segments 
(Fig.  195).  The  division  into  segments  may  be  made  more  conspicu- 
ous by  placing  on  the  wire,  before  bowing  it,  narrow  V-shaped  pieces 
of  paper,  or  riders.  If,  for  example,  the  cork  is  placed  at  one  fourth 


FIGURE  194.  —  STRING  VIBRATING  IN  SEG- 
MENTS. 


FIGURE  195.  —  WIRE  VIBRATING  IN  SEGMENTS. 

the  length  of  the  wire,  the  paper  riders  should  be  in  the  middle,  and  at 
one  fourth  the  length  from  the  other  end,  and  at  points  midway  be- 
tween these.  When  the  wire  is  deftly  bowed,  the  riders  at  the  fourths 
will  remain  seated,  and  the  intermediate  ones  will  be  thrown  off. 
The  latter  mark  points  of  maximum,  and  the  former  those  of  mini- 
mum vibration. 

The  ends  of  a  wire  and  the  intermediate  points  of  least 
motion  are  called  nodes ;  the  vibrating  portions  between 


204  SOUND 

the  nodes  are  loops  or  segments;  and  the  middle  points  of 
the  loops  are  called  antinodes.  The  last  two  experiments 
illustrate  what  are  known  as  stationary  waves.  They 
result  from  the  interference  of  the  direct  system  of  waves 
and  those  reflected  from  the  fixed  end  of  the  wire.  At 
the  nodes  the  two  meet  in  opposite  phase;  at  the  anti- 
nodes  in  the  same  phase.  At  the  former  the  motion  is  re- 
duced to  a  minimum  ;  at  the  latter  it  rises  to  a  maximum. 

233.  Overtones  in  Strings.  —  Stretch  two  similar  wires  on  the 
sonometer  and  tune  to  unison;  then  place  a  movable  bridge  at  the 

middle  of  one  of  them.     Set  the 
longer  wire  in  vibration  by  pluck- 
ing or  bowing  it  near  one  end. 
FIGURE  196.  -  FUNDAMENTAL  AND  Oc-    The  tone  mogt  distinctl    heard  is 

TAVE  TOGETHER.  J 

its  fundamental.    Touch  the  wire 

lightly  at  its  middle  point ;  instead  of  stopping  the  sound,  a  tone  is  now 
heard  in  unison  with  that  given  by  the  shorter  wire,  that  is,  an  octave 
higher  than  the  fundamental  and  caused  by  the  longer  wire  vibrating 
in  halves  (Fig.  196).  If  the  wire  be  again  plucked,  both  the  funda- 
mental and  the  octave  may  be 
heard  together. 

Touching   the  wire  one  third 
from  the  end  brings  out  a  tone  in     FlGURE  19£  ~  FUNDAMENTAL  AND  Oc- 

...     ,,    J      .          ,       ,,  TAVE  PLUS  FIFTH  TOGETHER. 

unison   with  that  given  by  the 

second  wire  reduced  to  one  third  its  length  by  the  movable  bridge, 
that  is,  it  yields  a  tone  of  three  times  the  frequency,  or  an  octave  and 
a  fifth  higher  than  the  fundamental.  Figure  197  illustrates  the  man- 
ner in  which  the  wire  is  vibrating. 

The  experiment  shows  that  a  wire  may  vibrate  not  only 
as  a  whole  but  at  the  same  time  in  parts,  yielding  a  com- 
plex note.  The  tones  produced  by  a  body  vibrating  in 
parts  are  called  overtones  or  partial  tones. 

234.  Harmonics.  —  If  the  frequency  of  vibration  of  the 
overtone  is  an  exact  multiple  of  the  fundamental,  it  is 
called  an  harmonic  partial  or  simply   an    harmonic.     In 


AIR  AH  A    SOURCE  OF  SOUND 


205 


strings  the  overtones  are  usually  harmonics,  but  in  vibrat- 
ing plates  and  membranes  they  are  not. 

The  harmonics  are  named  first,  second,  third,  etc.,  in 
the  order  of  their  vibration  frequency.  The  frequency  of 
any  particular  harmonic  is  found  by  multiplying  that  of 
the  fundamental  by  a  number  one  greater  than  the  number 
of  the  harmonic.  For  example,  the  frequency  of  the  first 
harmonic  of  c1  of  256  vibrations  per  second  is  256  X  2  = 
512 ;  that  of  the  second  is  256  x  3  =  768,  etc. 

X.     VIBRATION  OF  AIR  IN  PIPES 

235.  Air  as  a  Source  of  Sound.  — In  the  use  of  the  res- 
onator we  saw  that  air  may  be  thrown  into  vibration  when 


FIGURE  198.  —  CLARINET. 

it  is  confined  in  tubes  or  globes,  and  that  it  thus  becomes 
the  source  of   sound.     Such  a  body  of  air  may  be    set 


FIGURE  199.  —  FLUTE. 

vibrating  in  two  ways;    by  a  vibrating  tongue  or  reed, 
as  in  the  clarinet  (Fig.  198),  the  fish  horn,  etc.,  or  by  a 


FIGURE  200.  —  TROMBONE. 

stream  of  air  striking  against  the  edge  of  an  opening  in 
the  tube,  as  in  the  whistle,  the  flute  (Fig.  199),  the  organ 
pipe,  etc.  In  several  pipe  or  wind  instruments  the  lips 


206 


SOUND 


of  the  player  act  as  reeds,  as  in  the  trumpet,  trombone 
(Fig.  200),  the  French  horn,  and  the  cornet.  Wind 
instruments  may  be  classed  as  open  or  stopped  pipes, 
according  as  the  end  remote  from  the  mouthpiece  is  open 
or  closed. 

236.  Fundamental  of  a  Closed  Pipe.  — Let  the  tall  jar  of 
Fig.  201  be  slowly  filled  with  water  until  it  responds  strongly  to  a 

c'  fork,  for  example.  The  length  of  the  column  of 
air  will  be  about  13  in.  or  one  fourth  of  the  wave 
length  of  the  note. 

When  the  prong  at  a  moves  to  b,  it  makes  half 
a  vibration,  and  generates  half  a  sound  wave.  It 
sends  a  condensed  pulse  down  the  tube  AB,  and 
this  pulse  is  reflected  from  the  water  at  the  bot- 
tom. Now,  if  AB  is  one  fourth  a  wave  length,  the 
distance  down  and  back  is  one  half  a  wave  length, 
and  the  pulse  will  return  to  A  at  the  instant  when 
the  prong  begins  to  move  from  b  back  to  a,  and  to 
send  a  rarefaction  down  AB.  This  in  turn  will 
FIGURE ^201.  — -  run  down  the  tube  and  back,  as  the  prong  com- 
pletes its  vibration ;  the  co- vibration  is  then  re- 
peated indefinitely,  the  tube  responds  to  the  fork, 
and  its  length  is  one  quarter  of  the  wave  length.  Hence, 

The  fundamental  of  a  closed  pipe  is  a  note  whose  wave 
length  is  four  times  the  length  of  the  pipe. 

237.  Laws  for  Columns  of  Air.  —  Set  vertically  in  a  wooden 
base  eight  glass  tubes  each  about  25  cm.  long  and  2  cm.  in  diameter 
(Fig.  202).     Pour  in  them  melted  paraffin  to  close  the  bottom.     A 
musical  note  may  be  produced  by  blowing  a  stream  of  air  across  the 
top  of  each  tube.     From  the  confused  flutter  made  by  the  air  striking 
the  edge  of  the  tube,  the  column  of  air  selects  for  reenforcement  the 
frequency  corresponding  to  its  own  rate.     Hence  the  pitch  may  be 
varied  by  pouring  in  water.     Adjust  all  the  tubes  with  water  until  they 
give  the  eight  notes  of  the  major  diatonic  scale .     The  measured  lengths 
of  the  columns  of  air  will  be  found  to  be  nearly  as  1,  f,  |,  $,  f,  f,  •&,  £. 


STATE  OF  THE  AIR  IN  A   SOUNDING  PIPE       207 


The  notes  emitted  have  the 
frequencies  1,  f ,  f ,  f,  f,  f,  V> 
2  (§  224).  Hence, 

The  frequency  of  a  vi- 
brating column  of  air  is 
inversely  as  its  length. 

This  is  the  principle 
employed  in  playing  the 
trombone. 


FIGURE  202.  —  PIPES  FOR  NOTES  OF 
MAJOR  DIATONIC  SCALE. 


Blow  gently  across  the  end 
of  an  open  tube  30 

cm.  long  and  about  2  cm.  in  diameter  arid  note  the  pitch. 
Take  another  tube  of  the  same  diameter  and  15  cm.  long ; 
stop  one  end  by  pressing  it  against  the  palm  of  the  hand, 
and  sound  it  by  blowing  across  the  open  end.  The  pitch 
of  the  closed  pipe  will  be  the  same  as  that  of  the  open  one. 
The  experiment  may  be  varied  by  comparing  the  notes  ob- 
tained by  the  shorter  pipe  when  open  and  when  closed  at 
one  end;  the  former  will  be  an  octave  higher  than  the 
latter.  Hence, 

For  the  same  frequency,  the  open  pipe  is  twice 
the  length  of  the  stopped  one. 

The  length  of  the  open  pipe  is,  therefore,  half 
the  wave  length  of  the  fundamental  note  in  air. 

238.   State   of   the  Air   in   a   Sounding   Pipe. — 

Employing  an  open  organ  pipe,  preferably  with  one  glass 
side  (Fig.  203),  lower  into  it  a  miniature  tambourine  about 
3  cm.  in  diameter  and  covered  with  fine  sand,  while  the 
pipe  is  sounding  its  fundamental  note.     The  sand  will  be 
agitated   most   at  the   ends  of  the  pipe   and  very  little 
IGIJ   ^   at  the  middle.     There  is,  therefore,  a  node  at  the  middle 
NODE     AT   °^  an  °Pen  Pi?6-     -A.  node  is  a  place  of  least  motion  and 
MIDDLE  OF   greatest  change  of  density;    an   antinode   is   a  place   of 
PIPE.  greatest  motion  and  least  change  of  density.     The  closed 


*208  SOUND 

end  of  a  pipe  is  necessarily  a  node,  and  the  open  end  an  antinode 
Hence, 

In  an  open  pipe,  for  the  fundamental  tone,  there  is  a 
node  at  the  middle  and  an  antinode  at  each  end;  in  the 
stopped  pipe,  there  is  a  node  at  the  closed  end  and  an 
antinode  at  the  other  end. 

239.  Overtones  in  Pipes.  —  Blow  across  the  open  end  of  a  glass 
tube  about  75  cm.  long  and  2  cm.  in  diameter.     A  variety  of  tones 
of  higher  pitch  than  the  fundamental  may  be  obtained  by  varying 
the  force  of  the  stream  of  air. 

These  tones  of  higher  pitch  than  the  fundamental  are 
overtones ;  they  are  caused  by  the  column  of  air  vibrating 
in  parts  or  segments  with  intervening  nodes. 

Open  pipes  give  the  complete  series  of  overtones,  with  fre- 
quencies 2,  3,  4>  5,  etc.  times  that  of  the  fundamental. 

In  stopped  pipes  only  those  overtones  are  possible  whose 
frequencies  are  3, 5,  7,  etc.  times  that  of  the  fundamental. 

Briefly,  the  reason  is  that  with  a  node  at  one  end  and  an 
antinode  at  the  other,  the  column  of  air  can  divide  into 
an  odd  number  of  equal  half  segments  only. 

It  follows  that  the  notes  given  by  open  pipes  differ  in 
quality  from  those  of  closed  pipes. 

XI.   GRAPHIC  AND  OPTICAL  METHODS 

240.  Record  of  Vibrations.  —  Graphic  methods  of  study- 
ing sound  are  of  service  in  determining  the  frequency  of 
vibration.     Figure  204  shows  a  practical  device  for  this 
purpose.     A  sheet  of   paper  is  wrapped  around  a  metal 
cylinder,  and  is  then  smoked  with  lampblack.     A  large 
fork  is  securely  mounted,  so  that. a  light  style  attached 
to  one  prong  touches  the  paper  lightly.     The  cylinder  is 


MANOMETRIC  FLAMES 


209 


mounted  on  an  axis,  one  end  of  which  has  a  screw  thread 

cut  in  it,  so  that  when  the  cylinder  turns  it  also  moves 

in   the  direction  of  its 

axis.     The   beats   of   a 

seconds  pendulum  may 

be  marked  on  the  paper 

by    means    of    electric 

sparks  between  the  style 

and  the  cylinder.     The 

number   of    waves    be- 
tween successive  marks 

made   by  the  spark   is 

equal  to  the  frequency    FIGURE  204.  —  INSCRIBING  THE  VIBRATIONS 

of  the  fork.  OF  A  FORK- 

241.   Manometric  Flames.  —  A   square   box  with  mirror 

faces   is   mounted  so   as  to  turn  around  a   vertical   axis 

(Fig.  205).  In  front  of  the  revolving  mirrors  is  sup- 
ported a  short  cylinder 
A.,  which  is  divided  into 
two  shallow  chambers 
by  a  partition  of  gold- 
beater's skin  or  thin  rub- 
ber. Illuminating  gas 
is  admitted  to  the  com- 
partment on  the  right 
through  the  tube  with  a 
stop-cock,  and  burns  at 
the  small  gas  jet  on  the 
little  tube  running  into 

FIGURE  205.  — MANOMETRIC    FLAME    AP-    this  same  compartment. 

PARATUS.  rr(1 

The    speaking    tube    is 

connected  to  the  compartment  on  the  other  side  of  the 
flexible  partition. 


210 


SOUND 


FIGURE  206.  —  MANOMETRIC  FLAMES.       ,, 

now  of  gas 

to  the  burner.  The  flame  changes  shape 
and  flickers,  but  its  vibrations  are  too  rapid 
to  be  seen  directly.  But  if  it  is  examined 
by  reflection  from  the  rotating  mirrors,  its 
image  is  a  serrated  band  (Fig.  206). 

Koenig  fitted  three  of  these  little  cap- 
sules with  jets  to  the  side  of  an  open  organ 
pipe  (Fig.  207),  the  membrane  on  the  inner 
side  of  the  gas  chamber  forming  part  of 
the  wall  of  the  pipe.  When  the  pipe  is 
blown  so  as  to  sound  its  fundamental  tone, 
the  middle  point  is  a  node  with  the  great- 
est variations  of  pressure  in  the  pipe,  and 
the  flame  at  that  point  is.  more  violently 
agitated  than  at  the  other  two,  giving  in 
the  mirrors  the  top  band  of  Fig.  206.  By 
increasing  the  air  blast,  the  fundamental 
is  made  to  give  way  to  the  first  overtone ; 
the  two  outside  jets  then  vibrate  most 
strongly,  and  give  the  second  band  in  the 
figure,  with  twice  as  many  tongues  of  flame 


When  the  mirrors  are 
turned,  the  image  of  the 
gas  jet  is  drawn  out  into 
a  smooth  band  of  light. 
Any  pure  tone  at  the 
mouthpiece  produces  alter- 
nate compressions  and  rare- 
factions in  both  chambers 
separated  by  the  mem- 
brane, and  these  aid  and 
retard  the 


FIGURE  207.  — 
ORGAN  PIPE  WITH 
GAS  FLAMES. 


THE  PHONODEIK 


211 


as  in  the  image  for  the  fundamental.     The  third  band 

may  be  obtained  by  adjusting  the  air  pressure  so  that  both 

the  fundamental  and  the  first  overtone  are  produced  at  the 

same  time.     This  same 

figure  may  be  obtained 

by     singing     into     the 

mouthpiece  or  funnel  of 

Fig.  205  the  vowel  sound 

o  on  the  note  B,  showing 

that  this  vowel  sound  is 

composed    of    a    funda-  FlGURE  208.  — THE  PHONODEIK. 

mental  and  its  octave. 

242.   The  Phonodeik  is  an  instrument  devised  by  Professor 

Dayton  C.  Miller  to  exhibit  sound  waves.     It  consists  of 

a  very  small  and  thin  glass  mirror  mounted  on  a  minute 

steel  spindle  resting  in  jeweled 
bearings.  On  this  spindle  is  a 
little  pulley  around  which  wraps 
a  fine  thread.  One  end  of  the 
thread  is  attached  to  a  very  thin 
glass  diaphragm  closing  the 

small  end  of  a  resonator  horn  ;   the  other  is  connected  to 

a  delicate  tension  spring  (Fig.  208).     A  small  pencil  of 

light  is  focused  on  the  mirror  by  a  lens  and  is  reflected  by 

the  mirror  to  a  sensitized  film 

moving   at  right  angles   to  it. 

Any  vibration  of  the  diaphragm 

traces  on  the  film  a  wave  form 

marked  with  all  the  perculiari-  FlGURE  210.  — WAVE   FORM   OF 

.     ,  _          j      .  VIOLIN  TONE. 

ties  of  the  sound  producing  the 

vibrations  of  the  diaphragm.  These  photographs  are  af- 
terwards enlarged.  Fig.  209  shows  the  wave  form  caused 
by  a  heavy  tuning  fork.  Fig.  210  represents  the  wave  of 


FIGURE  209.  — WAVE  FORM  FROM 
TUNING  FORK. 


212  SOUND 

a  violin  tone,  the  irregulari- 
ties marking  the  overtones. 
Fig.  211  is  the  wave  form  of 

the  sound  of  the  human  voice 
FIGURE  211. — WAVE    FORM    OF  . 

VOICE.  saying  "  ah. 

Questions  and  Problems 

1.  Name  three  ways  in  which  musical  sounds  may  differ. 

2.  Pianos  are  made  so  that  the  hammers  strike  the  wires  near  one 
end  and  not  in  the  middle.     Why? 

3.  Why  does  the  pitdh  of  the  sound  made  by  pouring  water  into  a 
tall  cylindrical  jar  rise  as  the  jar  fills? 

4.  What  effect  does  a  rise  of  temperature  have  on  the  pitch  of  a 
given  organ  pipe  ?    Explain. 

5.  If  the  pipes  of  an  organ  are  correctly  tuned  at  a  temperature 
of  40°  F.,  will  they  still  be  in  tune  at  90°  F.  ?    Explain. 

6.  The  tones  of  three  bells  form  a  major  triad.     One  of  them 
gives  a  note  a  of  220  vibrations  per  second,  and  its  pitch  is  between 
those  of  the  other  two.     What  are  the  frequencies  of  three  bells, 
and  what  is  the  note  given  by  the  highest? 

7.  How  much  must  the  tension  of  a  violin  string  be  increased  to 
raise  its  pitch  a  fifth  (§  223)  ? 

8.  If  the  E  string  of  a  violin  is  40  cm.  long,  how  long  must  a 
similar  one  be  to  give  G  ? 

9.  The  vibration  frequency  of  two  similar  wires  100  cm.  long  is 
297.     How  many  beats  per  second  will  be  given  by  the  two  wires 
when  one  of  them  is  shortened  one  centimeter  ? 

10.  Two  c'  forks  gave  5  beats  per  second  when  one  of  them  was 
weighted  with  bits  of  sealing  wax.     Find  the  frequency  of  the  weighted 
fork. 

11.  What  will  be  the  length  of  a  stopped  organ  pipe  to  give  c'  of 
256  vibrations  per  second  when  the  temperature  of  the  air  is  20°  C.? 

12.  Calculate  the  length  of  an  open  organ  pipe  whose  fundamental 
tone  is  one  of  32  vibrations  per  second,  and  the  temperature  of  the  air 
is20°C. 


QUESTIONS  AND  PROBLEMS  213 

13.  An  open  organ  pipe  sounds  c'  (256) ;  what  notes  are  its  two 
lowest  overtones? 

14.  What  is  the  frequency  of  an  8-foot  stopped  pipe  when  the 
velocity  of  sound  is  1120  ft.  per  second? 

15.  Two  open  organ  pipes  2  ft.  in  length  are  blown  with  air  at  a 
temperature  of  15°  and  20°  C.,  respectively.     How  many  beats  do  they 
give  per  second? 

16.  When  the  temperature  of  the  air  is  such  that  the  velocity  of 
sound  is  1105  ft.  per  second,  what  will  be  the  frequency  of  the  funda- 
mental note  produced  by  blowing  across  one  end  of  a  tube  12.75  in. 
long,  the  other  end  being  closed?    What  will  be  the  frequency  of  its 
first  overtone? 


CHAPTER   VIII 

LIGHT 
I.     NATURE  AND   TRANSMISSION  OF  LIGHT 

243.  The  Ether.  —  Exhaust  the  air  as  far  as  possible  from  a  glass 
bell  jar.     Place  a  candle  on  the  far  side  of  the  jar ;  it  will  be  seen  as 
clearly  before  the  air  has  been  let  into  the  bell  jar  as  after. 

It  is  obvious  that  the  medium  conveying  light  is  not  the 
air  and  it  must  be  something  that  exists  even  in  a  vacuum. 
This  medium  is  vaguely  known  as  the  ether.  It  exists 
everywhere,  even  penetrating  between  the  molecules  of 
ordinary  matter. 

244.  Light.  —  The  prevailing  view  about  the  nature  of 
light  is  that  it  is  a  transverse  wave  motion  in  the  ether. 
Huyghens,  a  Dutch  physicist,  in  1678  proposed  the  theory 
that  light  is  a  wave  motion;    later,   Fresnel,   a   French 
physicist,  showed  that  the  disturbance  must  be  transverse ; 
finally  Maxwell  modified  the  theory  to  the  effect  that  these 
disturbances  are  probably  not  transverse  physical  movements 
of  the  ether,  but  transverse  alterations  in  its  electrical  and 
magnetic  conditions. 

245.  Transparent  and  Opaque  Bodies.  —  When  light  falls 
on  a  body,  in  general,  a  part  of  it  is  reflected,  a  part  passes 
through  or  is  transmitted,  and  the  rest  is  absorbed.     A 
body  is  transparent  when  it  allows  light  to  pass  through  it 
with  so  little  loss  that  objects  can  be  easily  distinguished 
through  it,  as  in  the  case  of  clear  glass,  air,  pure  water. 
Translucent  bodies  transmit  light,  but  so  imperfectly  that 

214 


NIAGARA  FALLS  POWER  PLANT. 
Used  for  light  and  power  in  several  cities  of  New  York  State. 


SPEED  OF  LIGHT 


215 


objects  cannot  be  seen  distinctly  through  them,  as  horn, 
oiled  paper,  very  thin  sheets  of  metal  or  wood.  Other 
bodies,  such  as  blocks  of  wood  or  iron,  transmit  no  light, 
and  these  are  opaque.  No  sharp  line  of  separation  between 
these  classes  can  be  drawn.  The  degree  of  transparency 
or  opacity  depends  on  the  nature  of  the  body,  its  thick- 
ness, and  the  wave  length  (§  310)  of  the  light.  Water 
when  deep  enough  cuts  off  all  light;  the  bottom  of  the 
deep  ocean  is  dark.  Stars  invisible  at  the  foot  of  a  moun- 
tain are  often  visible  at  the  top ;  bodies  opaque  to  light  of 
one  wave  length  are  often  transparent  to  light  of  a  differ- 
ent wave  length. 

246.  Speed  of  Light.  —  Previous  to  the  year  1676  it  was 
believed  that  light  traveled  infinitely  fast,  because  no  one 
had  found  a  way 
to  measure  so 
great  a  velocity. 
But  in  that  year 
Roemer,ayoung 
Danish  astron- 
omer, made  the 
very  important 
discovery  that 
light  travels  with 
finite  speed. 
Roemer  was  en- 
gaged at  the 
Paris  Observa- 
tory in  observing  the  eclipses  of  the  inner  moon  of  the 
planet  Jupiter.  At  each  revolution  of  the  moon  M  (Fig. 
212)  in  its  orbit  around  the  planet  J,  it  passes  into  the 
shadow  of  the  planet  and  becomes  invisible  from  the  earth 
at  E,  or  is  eclipsed.  By  comparing  his  observations  with 


FIGURE  212.  —  SPEED  OF  LIGHT  FROM  JUPITER'S 
INNER  MOON. 


216  LIGHT 

much  earlier  recorded  ones,  Roemer  found  that  the  mean  in- 
terval of  time  between  two  successive  eclipses  was  42.5 
hours.  From  this  it  was  easy  to  calculate  in  advance  the 
time  at  which  succeeding  eclipses  would  occur.  But  when 
the  earth  was  going  directly  away  from  Jupiter,  as  at  Uv  the 
eclipse  interval  was  found  to  be  longer  than  anywhere  else ; 
and  at  272,  across  the  earth's  orbit  from  Jupiter,  each  eclipse 
occurred  about  1000  sec.  later  than  the  predicted  time. 
To  account  for  this  difference  Roemer  advanced  the  theory 
that  this  interval  of  1000  sec.  is  the  time  taken  by  light 
to  pass  across  the  diameter  of  the  earth's  orbit.  This  gave 
for  the  speed  of  light  309  million  meters,  or  192,000  miles 
per  second. 

Later  determinations  in  our  own  country  by  Michelson 
and  Newcomb  show  that  the  speed  of  light  is  299,877  km., 
or  186,337  mi.  per  second. 

247.  Direction    of    Propagation.  —  Place  a  sheet-iron  cylinder 
over  a  strong  light,  such  as  a  Welsbach  gas  lamp,  in  a  darkened  room. 
The  cylinder  should  have  a  small  hole  opposite  the  light.     Stretch  a 
heavy  white  thread  in  the  light  streaming  through  the  aperture. 
When  the  thread  is  taut  it  is  visible  throughout  its  entire  length,  but 
if  permitted  to  sag  it  becomes  invisible. 

The  experiment  shows  that  light  travels  in  straight  lines. 
It  will  appear  later  that  this  is  true  only  when  the  medium 
through  which  light  passes  has  the  same  physical  proper- 
ties in  all  directions. 

248.  Bay,  Beam,  Pencil.  —  Light  is  propagated  outward 
from  the  luminous  source  in  concentric  spherical  waves, 
as  sound  waves  in  air  from  a  sonorous  body.     Rays  are 
the  radii  of  these  spherical  waves,  and  they  are,  therefore, 
normal  (perpendicular)  to  them.     They  mark  the  direc- 
tion of  propagation. 

When  the  source  of  light  is  at  a  great  distance,  the  rays 


SHADOWS  217 

incident  on  any  surface  are  sensibly  parallel.  A  number 
of  parallel  rays  form  a  beam  of  light.  For  example,  in  the 
case  of  light  from  the  sun  or  stars,  the  distance  is  so  great 
that  the  rays  are  sensibly  parallel.  Rays  of  light  pro- 
ceeding outward  from  a  point  form  a  diverging  pencil; 
rays  proceeding  toward  a  point,  a  converging  pencil. 

249.  Shadows.  —  Place  a  ball  between  a  lighted  lamp  and  a  white 
screen.  From  a  part  of  this  screen  the  light  will  be  wholly  cut  off, 
and  surrounding  this  area  is  one  from  which  the  light  is  excluded  in 
part.  If  three  small  holes  be  made  in  the  screen,  one  where  it  is 
darkest,  one  in  the  part  where  it  is  less  dark,  and  one  in  the  lightest 
part,  it  will  be  found  when  one  looks  through  them  that  the  flame  of 
the  lamp  is  wholly  invisible  through  the  first,  a  part  of  it  is  visible 
through  the  second,  and  the  whole  flame  through  the  third. 

The  space  behind  the  opaque  object  from  which  the 
light  is  excluded  is  called  the  shadow.  The  figure  on 
the  screen  is  a  section  of  the  shadow.  The  darkest  part 
of  the  shadow,  called  the  umbra,  is  caused  by  the  total 
exclusion  of  the  light  by  the  opaque  object ;  the  lighter 
part,  caused  by  its  partial  exclusion,  is  called  the  penumbra. 


p 
FIGURE  213.  —  SOURCE  OF  LIGHT  A  POINT. 

When  the  source  of  light  is  a  point  L  (Fig.  213),  the 
shadow  will  be  bounded  by  a  cone  of  rays,  ALB,  tangent 
to  the  object,  and  will  have  only  one  part,  the  umbra. 
When  the  source  of  light  is  an  area,  such  as  LL  (Fig.  214), 
the  space  ABDO  behind  the  opaque  body  receives  no  light, 
and  the  parts  between  AC  and  AQ' ,  and  between  BD  and 


218 


LIGHT 


BD{ r,  receive  some  light,  the  amount  increasing  as  AC' 
and  BD1  are  approached.  From  these  figures  the  cases 
when  the  luminous  body  is  larger  than  the  opaque  body, 


FIGURE  214.  —  SOURCE  OF  LIGHT  AN  AREA. 

and  when  it  is  of  the  same  size,  may  be  understood  and 
illustrated  by  the  student. 

250.  Images  by  Small  Openings.  —  Support  two  sheets  of  card- 
board (Fig.  215)  in  vertical  and  parallel  planes.  In  the  center  of  one 

cut  a  hole  H  about  2mm. 
square  and  in  front  of  it  place 
a  lighted  candle  or  lamp.  An 
inverted  image  of  the  flame 
will  appear  on  the  other  sheet 
if  the  room  is  dark.  The  area 
of  the  image  will  vary  with  any 

FIGURE  215.  —  IMAGE  BY  SMALL  OPENING.      chan§e  in  the  Position  of  the 

screen  or  candle,  the  bright- 
ness with  the  size  of  the  aperture,  but  no  change  in  the  shape  of  the 
aperture,  affects  the  image.  With  a  larger  aperture  the  image  gains 
in  brightness  but  loses  in  definition. 

Every  point  of  the  candle  flame  is  the  vertex  of  a  cone 
of  rays,  or  a  diverging  pencil,  passing  through  the  opening 
and  forming  an  image  of  it  on  the  screen.  These  numer- 
ous pictures  of  the  opening  overlap  and  form  a  picture  of 
the  flame,  and  the  number  at  any  one  place  determines 
the  brightness.  The  edge  of  the  image  will  therefore  be 
less  bright  than  other  portions.  In  the  case  of  a  large 


LAW  OF  INTENSITY  219 

opening,  the  overlapping  of  the  images  of  the  aperture 
destroys  all  resemblance  between  the  image  and  the  object, 
the  resulting  image  having  the  shape  of  the  aperture. 

251.  Illustrations. — The  pinhole  camera  is  an  applica- 
tion of  the  foregoing  principle.  It  consists  of  a  small 
box,  blackened  within,  and  provided  with  a  small  opening 
in  one  face  (Fig.  21*6)  ;  the  light  passes  through  this  and 
forms  an  image  on  the  sensitized  plate  placed  on  the  oppo- 


FIGURE  216.  —  PINHOLE  CAMERA. 


site  side.  When  the  sun  shines  through  the  small  chinks 
in  the  foliage  of  a  tree,  a  number  of  round  or  oval  spots 
of  light  may  be  seen  on  the  ground.  These  are  images  of 
the  sun.  During  a  partial  solar  eclipse  such  figures  as- 
sume a  crescent  shape. 

II.   PHOTOMETRY 

252.  Law  of  Intensity.  —  The  intensity  of  illumination  is 
the  quantity  of  light  received  on  a  unit  of  surface.  Every- 
day experience  shows  that  it  varies,  not  only  with  the 
source  of  the  light,  but  also  with  the  distance  at  which 
the  source  is  placed. 

Cut  three  cardboard  squares,  4,  8,  and  12  cm.  on  a  side  respectively, 
and  mount  them  on  supports  (Fig.  217).  The  centers  of  these  screens 
should  be  at  the  same  distance  above  the  table  as  the  source  of  light. 


220 


LIGHT 


Use  a  Welsbach  gas  lamp  with  an  opaque  chimney  having  a  small 
opening  opposite  the  center  of  the  light,  and  set  it  99  cm.  from  the 
largest  screen.  Place  the  medium-sized  screen  so  that  it  exactly  cuts 
off  the  light  from  the  edges  of  the  largest.  In  like  manner  place  the 
smallest  screen  with  respect  to  the  intermediate  one.  If  these  screens 
are  placed  with  care,  it  will  be  found  that  their  distances  from  the 
light  are  33,  66,  and  99  cm.  respectively,  or  as  1:2:3.  Now  as  each 
screen  exactly  cuts  off  the  light  from  the  one  next  farther  away,  it 


FIGURE  217.  —  LAW  OF  INTENSITY  OF  ILLUMINATION. 

follows  that  each  receives  the  same  amount  of  light  from  the  source 
when  the  light  is  not  intercepted.  The  surfaces  of  the  screens  are  as 
1:4:9,  and  hence  the  quantity  of  light  per  unit  of  surface  must  be 
inversely  as  1 : 4 :  9,  the  square  of  1,  2,  and  3  respectively. 

This  experiment  shows  that  the  intensity  of  illumination 
varies  inversely  as  the  square  of  the  distance  from  the  source 
of  light.  If  the  medium  is  such  as  to  absorb  some  of  the 
light,  the  decrease  in  intensity  is  greater  than  that  ex- 
pressed by  the  law  of  inverse  squares. 

This  law  of  illumination  assumes  that  the  source  of 
light  is  a  point,  and  that  the  receiving  surface  is  at  right 
angles  to  the  direction  of  the  rays.  When  the  surface  on 
which  the  light  (and  heat)  falls  is  inclined,  the  intensity 
is  still  less.  In  northern  latitudes  the  earth  is  nearer  the 
sun  in  winter  than  in  summer,  but  the  intensity  of  the 
radiation  received  is  less  than  in  summer,  because  the  alti- 


THE  BUN  SEN  PHOTOMETER 


221 


tude  of  the  sun  at  noon  is  less,  that  is,  because  the  earth's 
surface  is  more  inclined  to  the  direction  of  the  radiations. 

253.  The  Bunsen  Photometer.  —  A  photometer  is  an  instru- 
ment for  comparing  the  intensity  of  one  light  with  that  of 
another.  The  principle  applied  is  a  consequence  of  the 
law  of  the  intensity  of  illumination ;  it  is  that  the  ratio 
of  the  intensities  of  two  lights  is  equal  to  the  square 
of  the  ratio  of  the  distances  at  which  they  give  equal 
illumination. 

In  the  Bunsen  photometer  a  screen  of  paper  A  (Fig. 
218),  having  a  translucent  spot  made  by  applying  a  little 


FIGURE  218.  —  BUNSEN  PHOTOMETER. 

hot  paraffin,  is  supported  on  a  graduated  bar  between  a 
standard  candle  B  and  the  light  0  to  be  compared  with 
it.  An  old  but  imperfect  standard  candle  is  the  light 
emitted  by  the  sperm  candle  of  the  size  known  as  "  sixes," 
when  burning  120  grains  per  hour.  The  photometer 
screen  is  usually  inclosed  in  a  box  open  toward  the  two 
lights,  and  back  of  it  are  two  mirrors  placed  with  their 
reflecting  sides  toward  each  other  in  the  form  of  a  V,  so 
that  the  observer  standing  by  the  side  of  A  can  see  both 
sides  of  the  screen  by  reflection  in  the  mirrors.  The 


222  LIGHT 

position  of  A  or  of  B  may  then  be  adjusted  until  both 
sides  of  the  screen  look  alike.  Then  the  intensity  of  0 
is  to  the  intensity  of  B  as  AC2  is  to  A£?. 

In  the  Joly  photometer  two  rectangular  blocks  of 
paraffin,  separated  by  a  sheet  of  tinfoil,  take  the  place  of 
the  sheet  of  paper.  When  the  lights  are  balanced  the 
edges  of  the  paraffin  blocks  are  equally  lighted. 

Questions  and  Problems 

1.  What  is  the  cause  of  an  eclipse  of  the  sun  ?     Explain  by  diagram 

2.  What  is  the  cause  of  an  eclipse  of  the  moon  ?     Explain  by  dia- 
gram. 

3.  Why  does  a  small  aperture  in  the  camera  give  a  more  sharply 
denned  image  than  a  large  one? 

4.  Why  is  a  larger  aperture  in  the  camera  necessary  for  a  snapshot 
than  for  a  time  exposure? 

5.  In  an  attempt  to  determine  the  height  of  a  tree  the  following 
data  were  obtained :    Length  of  the  tree's  shadow,  50  ft. ;  length  of  the 
shadow  of  a  vertical  10-f t.  pole,  4  ft.     What  is  the  height  of  the  tree  4 

6.  Two  lights,  25  and  100  c.p.  respectively,  are  placed  60  ft.  apart. 
Where  must  a  screen  be  placed  between  them  and  on  the  line  joining 
them  so  as  to  be  equally  illuminated  on  its  two  sides? 

7.  In  measuring  the  candle  power  of  a  lamp  the  following  data  were 
obtained :  Distance  of  the  standard  lamp  from  the  photometer  disk, 
20  cm. ;  distance  of  lamp,  120  cm.     What  is  the  candle  power? 

8.  If  a  book  can  be  read  at  a  distance  of  1  ft.  from  a  20  c.p.  electric 
lamp,  at  what  distance  from  a  60  c.p.  lamp  can  it  be  read  with  equal 
clearness  ? 

9.  The  picture  of  a  tree  taken  with  a  pinhole  camera  was  10  cm. 
long.     The  aperture  was  20  cm.  from  the  sensitive  plate  and  30  m. 
from  the  tree.     What  is  the  height  of  the  tree  ? 

10.  Two  Mazda  lamps  are  to  be  used  to  give  equal  illumination  to 
the  two  sides  of  a  screen.     One  of  them  is  20  c.p.  and  distant  8  ft. 
from  the  screen ;  the  other  is  40  c.p.     How  far  from  the  screen  must 
the  second  lamp  be  placed  to  secure  the  desired  illumination  ? 


LAW  OF  REFLECTION 


223 


11.  What  is  the  length  of  the  umbra  of  the  earth's  shadow,  the 
diameter  of  the  earth  arid  sun  being  8000  and  880,000  miles  respec- 
tively, and  the  distance  from  the  center  of  the  earth  to  that  of  the 
sun  being  93,000,000  miles  ? 

III.  EEFLECTION  OF  LIGHT 

254.  Regular  Reflection.  —  When  a  beam  of   light  falls 
on  a  polished  plane  surface,  the  greater  part  of  it  is  re- 
flected in  a  definite  di- 
rection.    This     reflec- 
tion is  known  as  regu- 
lar reflection.     In  Fig. 

219  a  beam  of  light  IB 
is  incident  on  the  plane 
mirror  B  and  is  re- 
flected as  BE.  IB  is 
the  incident  beam,  BR 
is  the  reflected  beam,  the 
angle  IBP  between  the  incident  beam  and  the  normal 
(perpendicular)  to  the  reflecting  surface  is  the  angle  of 
incidence,  and  the  angle  PBR  between  the  reflected  beam 
and  the  normal  is  the  angle  of  reflection. 

255.  Law  of  Reflection.  —  On  a  semicircular  board  are  mounted 
two  arms,  pivoted  at  the  center  of  the  arc  (Fig.  220).     One  arm 
carries  a  vertical  rod  P,  and  the  other  a  paper  tube  T  with  parallel 

threads  stretched 
across  a  diameter  at 
each  end.  A  plane 
mirror  Mis  mounted 
at  the  center  of  the 
semicircle,  with  its 
reflecting  surface 
parallel  to  the  di- 
ameter at  the  ends 
FIGURE  220.  —  LAW  OF  REFLECTION.  of  the  arc.  On  the 


FIGURE  219.  —  INCIDENCE  AND  REFLECTION. 


224 


LIGHT 


edge  of  the  semicircle  is  a  scale  of  equal  parts  with  the  zero  on  the 
normal  to  the  mirror.  Place  the  arm  P  in  any  desired  position  and 
move  the  arm  T  until  the  image  of  the  rod  in  the  mirror  is  exactly  in 
line  with  the  two  threads.  The  scale  readings  will  show  that  the  two 
arms  make  equal  angles  with  the  normal  to  the  mirror.  Hence, 

The  angle  of  reflection  is  equal  to  the  angle  of  inci- 
dence; and  the  incident  ray,  the  normal,  and  the  reflected 
ray  all  lie  in  the  same  plane. 

256.  Diffused  Reflection.  —  Cover  a  large  glass  jar  with  a  piece 
of  cardboard,  in  which  is  a  hole  about  1  cm.  in  diameter.  Fill  the 
jar  with  smoke,  and  reflect  into  it  through  the  hole  in  the  cover  a 
beam  of  sunlight.  The  whole  of  the  interior  of  the  jar  will  be 
illuminated. 

The  small  particles  of  smoke  floating  in  the  jar  furnish 
a  great  many  reflecting  surfaces ;  the  light  falling  on 
them  is  reflected  in  as  many  directions.  The  scattering  of 
light  by  uneven  or  irregular  surfaces  is  diffused  reflection. 
To  a  greater  or  less  extent  all  reflecting  surfaces  scat- 
ter light  in  the  same  way  as  the  smoke  particles.  Figure 

221  illustrates  in  an 
exaggerated  way  the 
difference    between 
a    perfectly  smooth 
surface      and      one 
FIGURE  221.  —  REGULAR  AND  DIFFUSED  REFLEC-     somewhat      uneven. 
TION-  It  is  by  diffused  re- 

flection that  objects  become  visible  to  us.  Perfect  reflec- 
tors would  be  invisible ;  it  is  almost  impossible  to  see  the 
glass  of  a  very  perfectly  polished  mirror.  The  trees,  the 
ground,  the  grass,  and  particles  floating  in  the  air  reflect 
the  light  from  the  sun  in  every  direction,  and  thus  fill  the 
space  about  us  with  light.  If  the  air  were  free  from  all 
floating  particles  and  gases,  the  sky  would  be  dark  in  all 


IMAGE  IN  A   PLANE  MIRROR 


225 


directions,  except  in  the  direction  of  the  sun  and  the  stars. 
This  conclusion  is  confirmed  by  aeronauts  who  have  reached 
very  high  altitudes,  where  there  was  almost  a  complete  ab- 
sence of  floating  particles. 

257.  Image  in  a  Plane  Mirror.  —  Any  smooth  reflecting 
surface  is  called  a  mirror.  A  plane  mirror  is  one  whose 
reflecting  surface  is  a  plane.  A  spherical  mirror  is  one 
whose  reflecting  surface  is  a  portion  of  a  sphere. 

Support  a  pane  of  clear  window  glass  in  a  vertical  position,  and 
place  a  red-colored  lighted  candle  back  of  it.  Place  a  white  un- 
lighted  candle  in  front.  Move  the  unlighted  candle  until  its  image 
in  the  glass  as  a  mirror  coincides  exactly  with  the  lighted  candle  seen 
through  the  glass.  The  distance  of  the  two  candles  from  the  mirror 
will  be  the  same. 

Let  A  be  a  luminous  point  in  front  of  a  plane  mirror 
222).     The  group  of  waves  included  between 


the  rays  AB  and  AC  after 

reflection  proceed  as  if  from 

Ar,  situated  on  the  normal 

AK  and  as  far  behind  the 

reflecting  surface  as  A  is  in 

front  of  it.     An  eye  placed 

at  DE  receives  these  waves 

as  if  they  came  directly  from 

a  source  A1.     The  point  A1 

is  called  the  image  of  A  in 

the  mirror  MN.    It  is  known 

as  a  virtual  image,  because 

the   light   only   appears    to 

come   from   it.     Therefore, 

the  image  of  a  point  in   a 

plane  mirror  is  virtual,  and  is  as  far  back  of  the  mirror  as  the 

point  is  in  front.     The  image  may  be  found  by  drawing 


A 

FIGURE  222. 


—  POSITION  OF  IMAGE  OF 
A  POINT. 


226 


LIGHT 


FIGURE  223. —  CONSTRUCTION 
IMAGE. 


from  the  point  a  perpendicular  to  the  mirror,  and  pro- 
ducing the  perpendicular  until  its  length  is  doubled. 

258.  Construction  for  an  Image  in  a  Plane  Mirror.  — As 
the  image  of  an  object  is  composed  of  the  images  of  its 
points,  the  image  may  be  located  by  finding  those  of  its 

points.  Let  AB  (Fig.  223) 
represent  an  object  in  front  of 
the  plane  mirror  MN.  Draw 
perpendiculars  from  A  and  B 
to  the  mirror  and  produce  them 
until  their  length  is  doubled. 
AB'  is  the  image  of  AB.  It 
is  virtual,  erect,  and  of  the 
same  size  as  the  object. 

An  image  in  a  plane  mirror 
is  reversed  from  right  to  left.  This  is  clearly  seen  when 
a  printed  page  is  held  in  front  of  a  mirror,  the  letters  all 
being  reversed,  or  perverted,  as  it  is  termed.  Otherwise 
the  image  is  so  like  the  object  that  illusions  are  produced, 
because  a  well-polished  mirror  itself  is  invisible. 

In  general,  the  image  in  a  plane  mirror  is  the  same  size 
as  the  object,  is  virtual,  and  is  as  far  back  of  the  mirror  as 
the  object  is  in  front. 

259.  Path  of  the  Rays  to  the  Eye.  —  It  is  important  to 
notice  that  the  image  of  any  fixed  object  is  fixed  in  space, 
and  is  entirely  independent  of  the  position  of  the  observer. 
The  paths  of  the  rays  for  the  image  for  one  observer  are 
not  the  same  as  those  for  another. 

Let  AB  (Fig.  224)  represent  an  object  in  front  of  the 
plane  mirror  MN.  Drop  perpendiculars  from  points  of 
the  object  to  the  mirror,  and  produce  them  until  their 
length  is  doubled.  In  this  manner  the  image  of  AB  is 
found  at  A' B' .  Let  E  and  E1  be  the  position  of  the  eye 


USES  OF  A  PLANE  MIRROR 


227 


FIGURE  224. —  PATH  OF  RAYS  TO 
THE  EYE. 


for  two  observers.  To  find  the  path  of  the  rays  entering 
the  eye  at  E,  draw  lines  from  A1  and  B'  to  E.  These 
lines  are  the  directions  in  which  the  light  enters  the  eye 
from  A1  and  B1  respectively. 
But  no  light  comes  from  be- 
hind the  mirror,  and  so  the  in- 
tersections of  these  lines  with 
the  mirror  are  the  points  where 
the  rays  from  A  and  B  are  re- 
flected to  E.  In  a  similar  man- 
ner the  path  of  the  rays  may 
be  traced  for  the  position  of 
the  eye  at  E'.  The  full  lines 
in  front  of  the  mirror  are  the 
paths  of  the  rays  from  A  and 
B,  which  give  the  images  at 
A  and  B'. 

260.  Uses  of  a  Plane  Mirror.  —  The  employment  of  the 
plane  mirror  as  a  "  looking  glass  "  dates  from  a  period  of 
great  antiquity.  The  process  of  covering  a  glass  surface 
with  an  amalgam  of  tin  and  mercury  came  into  use  in 
Venice  about  three  centuries  ago.  The  process  of  cover- 
ing glass  with  a  film  of  silver  was  invented  during  the 
last  century. 

The  fact  that  the  image  in  a  plane  mirror  is  virtual  has 
been  used  to  produce  many  optical  illusions,  such  as  the 
stage  ghost,  the  magic  cabinet,  the  decapitated  head,  etc. 
To  produce  the  illusion  of  a  ghost,  a  large  sheet  of  un- 
silvered  plate  glass,  with  its  edges  hidden  by  curtains, 
is  so  placed  that  the  audience  has  to  look  obliquely 
through  it  to  see  the  actors  on  the  stage.  Other  actors, 
hidden  from  direct  view,  and  strongly  illuminated,  are  seen 
by  reflection  in  the  glass  as  ghostly  images  on  the  stage. 


228 


LIGHT 


261.   Multiple  Reflection.  —  Place  two  mirrors  so  that  their  re- 
flecting surfaces  form  an  angle  (Fig.  225).     If  a  lighted  candle  be 

placed  between  them,  several  images 
may  be  seen  in  the  mirrors;  three 
when  they  are  at  right  angles,  more 
when  the  angle  is  less  than  a  right 
angle.  When  the  mirrors  are  parallel, 
all  the  images  are  in  a  straight  line 

perpendicular  to  the  mirrors. 
FIGURE  225. —  MULTIPLE 

REFLECTION.  The     image     in     one     mirror 

serves  as  an  object  for  the  second  mirror,  and  the  image  in 
the  second  becomes  in  turn  an  object  for  the  first  mirror. 
In  Fig.  226  the  two  mirrors  are  at  right  angles.  Of  is  the 
image  of  0  in  AB,  and  is  found  as  in  §  258.  0'"  is  the 
image  of  0'  in  A  C,  and  is  found  by  the  line  0'  Oflf  drawn 
perpendicular  to  AC  produced.  0"  is  the  image  of  0  in 
A@,  and  since  the  mirrors  are 
at  right  angles,  0'"  is  also 
the  image  of  0"  in  AB.  0'" 
is  situated  behind  the  plane 
of  both  mirrors,  and  no  im- 
ages of  it  can  be  formed. 
All  the  images  are  situated 
in  the  circumference  of  a 
circle  whose  center  is  A  and 
radius  A  0.  If  E  is  the  po- 
sition of  the  eye,  then  0'  FIGURE  226. 
and  0"  are  each  seen  by  one 
reflection,  and  Orff  by  two  reflections,  and  for  this  reason 
it  is  less  bright.  To  trace  the  path  of  a  ray  for  the  image 
O'ri ',  draw  0"f  E,  cutting  AB  at  6,  and  from  the  intersec- 
tion "b  draw  10",  cutting  A 0 at  a.  Join  aO  ;  the  path  of 
the  ray  is  OabE.  It  is  interesting  to  find  the  images  when 
the  mirrors  are  at  various  angles. 


—  MIRRORS    AT  .RIGHT 
ANGLES. 


SPHERICAL  MIRRORS 


229 


262.  Illustrations.  —  The  double  image  of  a  bright  star  and  the 
several  images  of  a  gas  jet  in  a  thick  mirror  (Fig.  227)  are  examples 
of  multiple  reflection,  the  front  surface  of  the  mirror  and  the  metallic 
surface  at  the  back  serving  as  parallel  reflectors.     Geometrically  the 
number  of  images  is  infinite ; 

but  on  account  of  their  faint- 
ness  only  a  limited  number  is 
visible.  The  kaleidoscope,  a  toy 
invented  by  Sir  David  Brewster, 
is  an  interesting  application  of 
the  same  principle.  It  consists 
of  a  tube  containing  three  mir- 
rors extending  its  entire  length, 
the  angle  between  any  two  ol 
them  being  60°.  One  end  of  the 
tube  is  closed  by  ground  glass, 
and  the  other  by  a  cap  with  a 
round  hole  in  it.  Pieces  of 
colored  glass  are  placed  loosely 
between  the  ground  glass  and  a 
plate  of  clear  glass  parallel  to 
it.  On  looking  through  the 
hole  at  any  source  of  light, 
multiple  images  of  these  pieces 

of  glass  are  seen,  symmetrically  arranged  around  the  center,  and  form- 
ing beautiful  figures,  which  vary  in  pattern  with  every  change  in  the 
position  of  the  pieces  of  glass. 

263.  Spherical  Mirrors.  —  A  mirror  is  spherical  when  its 
reflecting  surface  is  a  portion  of  the  surface  of  a  sphere. 
If  the  inner  surface  is  polished  for  reflection,  the  mirror 

is  concave  ;  if  the  outer  surface,  it  is 
convex.  Only  a  small  portion  of  a 
spherical  surface  is  used  as  a  mirror. 
In  Fig.  228  the  center  0  of  the  mirror 
MN  is  the  center  of  curvature  of  the 

FIGURE  228.  SPHERICAL  SPhere  of  which  the  ^fleeting  surface 
MIRROR.  is  a  part.     The  middle  point  A  of  the 


FIGURE  227.  —  MULTIPLE  IMAGES. 


230  LIGHT 

reflecting  surface  MN  is  the  pole  or  vertex  of  the  mirror, 
and  the  straight  line  AB  passing  through  the  center  of 
curvature  Q  and  the  pole  A  of  the  mirror  is  its  principal 
axis.  Any  other  straight  line  through  the  center  and  in- 
tersecting the  mirror  is  a  secondary  axis.  The  figures  of 
spherical  mirrors  in  this  chapter  are  sections  of  a  sphere 
made  by  passing  a  plane  through  the  principal  axis. 

The  difference  between  a  plane  mirror  and  a  spherical 
one  is  that  the  normals  to  a  plane  mirror  are  all  parallel 
lines,  while  those  of  a  spherical  mirror  are  the  radii  of  the 
surface,  and  all  pass  through  the  center  of  curvature. 

264.  Principal  Focus  of  Spherical  Mirrors.  —  A  focus  is 
the  point  common  to  the  paths  of  all  the  rays  after  inci- 
dence. It  is  a  real  focus  if  the  rays  of  light  actually  pass 
through  the  point,  and  virtual  if  they  only  appear  to 
do  so. 

Let  the  rays  of  the  sun  fall  on  a  concave  spherical  mirror.  Hold  a 
graduated  ruler  in  the  position  of  its  principal  axis,  and  slide  along 
it  a  small  strip  of  cardboard.  Find  the 
point  where  the  image  of  the  sun  is  small- 
est. This  will  mark  the  principal  focus, 
and  it  is  a  real  one.  If  a  convex  spherical 
mirror  be  used  the  light  will  be  reflected 
as  a  broad  pencil  diverging  from  a  point 
back  of  the  mirror.  The  focus  is  then  a 
virtual  one. 

FIGURE  229.  —  PRINCIPAL 

Focus,  CONCAVE  MIRROR.         «  a  pencil  of  rays  parallel  to  the 

principal   axis   falls   on   a   concave 

spherical  mirror,  the  point  to  which  the  rays  converge  after 
reflection  is  called  the  principal  focus  of  the  mirror  (Fig. 
229).  In  the  case  of  a  convex  spherical  mirror,  the  prin- 
cipal focus  is  the  point  on  the  axis  behind  the  mirror  from 
which  the  reflected  rays  diverge  (Fig.  230).  The  dis- 


POSITION  OF  THE  PRINCIPAL  FOCUS 


231 


FIG.URE  230.  —  PRINCIPAL  Fo- 
cus, CONVEX  MIRROR. 


tance  of  the  principal  focus  from 
the  mirror  is  its  principal  focal 
length. 

265.  Position  of  the  Principal 
Focus.  —  Let  MN  (Fig.  231)  be 
a  concave  mirror  whose  center  is 
at  C  and  principal  axis  is  AB. 
Let  ED  be  a  ray  parallel  to  BA. 
Then  CD  is  the  normal  at  D; 
and  CDF,  the  angle  of  reflection,  must  equal  EDC,  the 
angle  of  incidence.  Since  the  ray  BA  is  normal  to  the 
mirror,  it  will  be  reflected  back 
along  AB.  The  reflected  rays  DF 
1  and  AB  have  a  common  point  F, 
which  is  the  principal  focus.  The 
triangle  CFD  is  isosceles  with  the 
sides  CF  and  FD  equal.  (Why  ?) 
But  when  the  point  D  is  near  A, 
FD  is  equal  to  FA  ;  F  is  therefore 
the  middle  point  of  the  radius  CA. 
Other  rays  parallel  to  BA  will  pass  after  reflection  nearly 
through  F.  Hence,  the  principal  focus  of  a  concave  spheri- 
cal mirror  is  real  and  is  halfway  between  the  center  of  curva- 
ture and  the  vertex. 

Let  MN  (Fig.  232)  be  a 
convex  spherical  mirror.  ED 
and  BA  are  rays  parallel  to 
the  principal  axis.  When 
produced  back  of  the  mirror, 
after  reflection,  their  common 
point  F  is  back  of  the  mirror 

and  half  way  bet  ween  ^4.  and  C.  ~         OQO     n 

TT  •  FIGURE  232.—  PRINCIPAL  Focus  VIR- 

.(Why  >)     Hence,  the  pmnci-         TUAL  FOR  CONVEX  MIRROR. 


FIGURE  231.  -  POSITION  OF 
PRINCIPAL  Focus. 


u 


_ 

F        c 


232 


LIGHT 


FIGURE  233.  —  CONJUGATE  Foci,  CONCAVE 
MIRROR. 


pal  focus  of  a  convex  spherical  mirror  is  virtual  and  halfway 

between  the  center  of  curvature  and  the  mirror. 

266.    Conjugate  Foci  of  Mirrors.  —  When  a  diverging  pen- 
cil of  light  AED  (Fig.  233)  falls  on  the  spherical  mirror 

MN,  it  is  focused  after 
reflection  at  a  point  B' 
on  the  axis  AB  which 
passes  through  the  ra- 
diant point  or  source 
of  light ;  after  reflec- 
tion the  rays  diverge 
from  this  focus  B1  as  a 

new  radiant  point.     When  rays  diverging  from  one  point 

converge  to  another,  the  two  points  are  called  conjugate 

foci. 

In  Fig.  234,  the  rays  BA  and  BD  diverge  from  B  as  the 

radiant  point ;    after  reflection   they  diverge  as  if  they 

came  from  B'  behind  the 

reflecting  surface  ;  B1  is 

a  virtual   focus  and  B 

and   B'    are    conjugate 

foci. 

In  the  first  case  the 

source  of  light  is  farther 

from  the  mirror  than  the 

center  of  curvature,  and  the  focus  is  real  ;  in  the  second 

case  it  is  nearer  the  mirror  than  the  principal  focus,  and 

the  focus  is  virtual.1 


FIGURE  234.  —  CONJUGATE  Foci,  ONE 
Focus  VIRTUAL. 


1  In  Fig.  233,  CD  bisects  the  angle  BDH.     Hence,  -  —  =  ^-.     If  D 

B' D     B' C 

is  close  to  A,  we  may,  without  sensible  error,  place   BD  =  BA  and 
B'D  =  B'A.    Put  BA  =  p,  B'A  =  g,   CA=r  =  2/.     Then  BC  =  p  -  r, 

B'  C  =  r  -  g,  and  -  =^37^,  from  which  -  +  -  =  -  =  j.     By  measuring  j) 


IMAGES  IN   SPHERICAL  MIRRORS 


233 


267.    Images  in  Spherical  Mirrors.  —  In  a  darkened  room  sup- 
port on  the  table  a  concave  spherical  mirror,  a  candle,  and  a  small 
white  screen.     Place  the  candle  anywhere  beyond  the  focus,  and  move 
the  screen  until  a  clear  image  of 
the  flame  is  formed  on  it  (Fig. 
235).   Notice  the  size  and  position 
of  the  image,  and  whether  it  is 
erect  or  inverted.     When  the  can- 
dle is  between  the  focus  and  the 
mirror,  an  image  of  it  cannot  be 
obtained  on  the  screen,  but  it  can 
be  seen  by  looking  into  the  mirror.      FlGURE  235-  ~  IMAGE  BY  CONCAVE 
The  same  is  true  for  the  convex  MIRROR. 

mirror,  whatever  be  the  position  of  the  candle ;  in  these  last  cases  the 
image  is  a  virtual  one. 

The   experiment   shows   the   relative   positions   of   the 
object  and  its  image  for  a  concave  mirror,  all  depending 

on  the  position  of 
the  object  with  re- 
spect to  the  mirror. 
If  these  positions 
are  carefully  noted 
it  will  be  seen  that 
there  are  six 


§ 


FIGURE  236.  —  OBJECT  BEYOND  CENTER  OF  CURVA-    £jnc£   cases   as    fol- 
TURE. 

lows : 

First.  —  When  the  object  (AB,  Fig.  236)  is  at  a  finite 
distance  beyond  the  center  of  curvature,  the  image  is  real, 
inverted,  smaller  than  the  object,  and  between  the  center 
of  curvature  and  the  principal  focus. 

Second.  —  When  a  small  object  is  at  the  center  of  curva^ 
ture,  the  image  is  real,  inverted,  of  the  same  size  as  the 


and  g,  we  may  compute  r  and  /.     For  the  convex  mirror,  q  and  r  are 
m 


234 


LIGHT 


FIGURE  237.— OB- 
JECT AT  CENTER  OF 
CURVATURE. 


object,  and  at  the  center  of  curvature 
(Fig.  237). 

Third.  —  When  the  object  is  between 
the  center  and  the  principal  focus,  the 
image  is  real,  inverted,  larger  than  the 
object,  and  is  beyond  the  center  (Fig. 
238).  This  is  the  converse  of  Case  I. 

Fourth.  —  When  the  object  is  at  the 
principal   focus,   the   rays   are    reflected 
parallel   and   no   distinct   image   is   formed    (Fig.   239). 

Fifth.  —  When  the  ob- 
ject is  between  the  prin- 
cipal focus  and  the  mir- 
ror, the  image  is  virtual, 
erect,  and  larger  than 
the  object  (Fig.  240). 

Sixth.  —  When  the 
mirror  is  convex,  the 
image  is  always  virtual, 
erect,  and  smaller  than 
the  object  (Fig.  241). 

268.  Construction  for 
Images.  —  To  find  images 
in  spherical  mirrors  by  geometrical  construction,  it  is  only 

necessary  to  find  conjugate 
focal  points.  To  do  this 
trace  two  rays  for  each  point 
for  the  object,  one  along  the 
secondary  axis  through  it, 
and  the  other  parallel  to  the 
principal  axis.  The  first  ray 
is  reflected  back  on  itself, 

FIGURE  239.  —  OBJECT  AT   PRINCI- 
PAL Focus.  and  the  second  through  the 


FIGURE  238.  —  OBJECT  BETWEEN  CENTER 
AND  PRINCIPAL  Focus. 


SPHERICAL  ABERRATION  IN  MIRRORS 


235 


FIGURE  240. —  OBJECT  BETWEEN 
PRINCIPAL  Focus  AND  MIRROR. 


principal  focus.     The  intersection  of  the  two  reflected  rays 

from  the  same  point  of  the  object  locates  the  image  of  that 

point. 

For  instance  :  In  Fig.  236, 

AC  is  the  path  of  both  the 

incident  and  the  reflected  ray, 

while  the  ray  AD  is  reflected 

through  the  principal  focus 

F.     Their  intersection  is  at 

a.     The  rays  B  0  and  BE  are 

reflected  similarly  through  b. 

Hence,   ab   is   the   image    of 

AB.     In   Fig.    240,  the   ray 

AC  along   the  secondary   axis,  and  AD  reflected   back 

through  F  as  DF,  must  be  produced  to  meet  back  of  the 

mirror  at  the  virtual  focus  a.     A  and  a  are  conjugate  foci ; 

also  B  and  £,  and  ab  is 
a  virtual  image. 

For  the  convex  mir- 
ror (Fig.  241)  the  con- 
struction is  the  same. 
From  the  point  A  draw 
A  C  along  the  normal  or 
secondary  axis,  and  AD 
parallel  to  the  principal 
axis.  The  latter  is  re- 
flected so  that  its  direc- 
tion passes  through  F. 

The  intersection  of  these  two  lines  is  at  a.     The  image 

ab  is  virtual  and  erect.  v 

269.  Spherical  Aberration  in  Mirrors.  —  Bend  a  strip  of  bright 
tin  into  as  true  a  semicircle  as  possible  and  fasten  it  to  a  vertical 
board  as  in  Fig.  242.  At  right  angles  to  the  board  at  one  end  place 


N 


FIGURE  241.  — IMAGE  ALWAYS  VIRTUAL  IN 
CONVEX  MIRROR. 


236 


LIGHT 


a  vertical  sheet  of  cardboard  containing  three  parallel  slots.  Send  a 
strong  beam  of  light  through  each  of  these  slots ;  the  three  beams  will 
be  reflected  by  the  curved  tin  through  different  points,  the  beam 

nearest  the  straight  rim 
of  the  mirror  crossing 
the  axis  nearest  the  mir- 


FIGURE  242.  —  SPHERICAL  ABERRATION. 


The  experiment 
shows  that  rays  in- 
cident near  the  mar- 
gin of  a  spherical 
mirror  cross  the  axis 
after  reflection  be- 
tween the  principal  focus  and  the  mirror.  This  spreading 
out  of  the  focus  is  known  as  spherical  aberration  by  reflec- 
tion. It  causes  a  lack  of  sharpness  in  the  outline  of 
images  formed  by  spherical  mirrors.  It  is  reduced  by 
decreasing  the  aperture  of  the  mirror  by  means  of  a  dia- 
phragm to  cut  off  marginal  rays, 

or   by  decreasing  the   curvature  of  .f —    < 

the  mirror  from  the  vertex  out- 
ward. The  result  then  is  a  para- 
bolic mirror  (Fig.  243),  which 
finds  use  in  searchlights,  light- 
houses, headlights  of  locomotives 
and  automobiles,  and  in  reflecting 
telescopes. 

270.   Caustics  by  Reflection.  —  Use 
the  tin  reflector  of  the  last  experi- 
ment as  shown  in  Fig.  244.     The  light  from  a  candle  or  a 
lamp  is  focused  on  a  curved  line. 

The  curve  formed  by  the  rays  reflected  from  a  spherical 
mirror  is  called  the  caustic  by  reflection.     It  may  be  seen 


\ 


\ 


FIGURE  243.  —  PARABOLIC 
MIRROR. 


QUESTIONS  AND  PROBLEMS  237 

by  letting  sunlight  fall  on  a  tin  milk  pail  partly  full  of 
milk,  or  on  a  plain  gold  ring  on  a  white  surface. 


FIGURE  244.  —  CAUSTIC  BY  REFLECTION. 

Questions  and  Problems 

1.  Why  is  the  image  of  an  object  seen  in  the  bowl  of  a  silver  spoon 
distorted  ? 

2.  Show  by  an  arrangement  of  plane  mirrors  how  to  see  around  an 
obstruction. 

3.  How  can  a  concave,  a  convex,  and  a  plane  mirror  be  distinguished 
from  one  another,  even  when  their  outer  surfaces  are  flat,  as  is  often 
the  case? 

4.  Construct  all  the  images  that  would  be  formed  of  a  luminous 
point  placed  between  two  mirrors  forming  an  angle  of  60°. 

5.  Show  by  a  diagram  that  a  person  can  see  his  whole  length  in  a 
short  plane  mirror  placed  on  a  vertical  wall  by  tipping  the  top  of  the 
mirror  forward  and  standing  close  to  the  mirror. 

6.  A   candle   foot   is  the   intensity    of    illumination   of  a   1  c.p. 
light  at  a  distance  of  one  foot  from  the  illuminated  surface.     What 
will  be  the  illumination  in  foot  candles  of  a  surface  10  ft.  away  from 
•a  50  c.p.  lamp? 


238  LIGHT 

7.  How  far  must  a  surface  be  from  a  40  c.p.  lamp  to  receive  the 
same  illumination  as  it  would  receive  from  a  4  c.p.  lamp  two  feet 
distant? 

8.  If  a  person  can  just  see  to  read  a  book  when  10  ft.  away  from  a 
16  c.p.  lamp,  how  far  away  from  a  1600  c.p.  arc  light  can  he  see  to 
read  the  book  ? 

9.  Where  must  a  16  c.p.  lamp  be  placed  between  two  parallel  walls 
of  a  room  20  ft.  apart  in  order  that  one  wall  may  be  four  times  as 
strongly  illuminated  as  the  other? 

10.  A  gas  burner  consuming  5  cu.  ft.  per  hour  gives  a  flame  of  16 
c.p.     A  16  c.p.  electric  bulb  consumes  44  watts  per  hour.     With  gas 
at  $  1  per  1000  cu.  ft.  and  electricity  at  12£  cents  per  K.  W.  hour, 
which  is  the  cheaper  ? 

11.  If  an  object  is  18  ft.  distant  from  a  concave  spherical  mirror 
and  the  image  formed  of  it  is  2  ft.  from  the  mirror,  what  is  its  focal 
length  ? 

12.  Find  by  a  diagram  what  effect  it  has  on  the  image  of  an  object 
in  a  convex  spherical  mirror  to  vary  the  distance  of  the  object  from 
the  mirror. 

13.  The  mirror  formula  applies  equally  well  to  the  convex  spheri- 
cal mirror  if  q,  r,  and /are  made  negative.     Find  the  position  of  the 
image  of  an  object  as  given  by  a  convex  spherical  mirror  when  the 

radius  of  curvature  is  20  inches, 
the  object  being  10  ft.  from  the 
mirror. 

14.  If  a  plane  mirror  is  moved 
parallel  to  itself  directly  away 
from  an  object  in  front  of  it, 
show  that  the  image  moves  twice 
as  fast  as  the  mirror. 

IV.   REFRACTION  OF  LIGHT 
271.  Refraction.  —  Fasten  a 

FIGURE 245. -REFRACTION  OF  LIGHT.     Pa?er  Profcractor  sc*le  centrally 

on  one  face  of  a  rectangular  bat- 
tery jar  (Fig.  245),  and  fill  the  jar  with  water  to  the  horizontal  di- 
ameter of  the  scale.  Place  a  slotted  cardboard  over  the  top.  With 


CAUSE  OF  REFRACTION 


239 


FIGURE  246.  —  CUP  OF  WATER 
AND  COIN. 


a  plane  mirror  reflect  a  beam  of  light  through  the  slit  into  the  jar,  at 
such  an  angle  that  the  beam  is  incident  on  the  water  exactly  back  of 
the  center  of  the  scale.  The  path  of  this  ribbon  of  light  may  be 
traced ;  its  direction  is  changed  at  the  surface  of  the  water. 

The   change  in   the   course  of  light  in   passing   from 
one  transparent  medium  into  another  is  called  refraction. 

Place  a  coin  at  the  bottom  of  an 
empty  cup  standing  on  a  table,  and 
let  an  observer  move  back  until  the 
coin  just  passes  out  of  sight  below  the 
edge  of  the  cup;  now  pour  water  into 
the  cup,  and  the  coin  will  come  into 
view  (Fig.  246). 

The  changes  in  the  apparent  depth 
of  a  pond  or  a  stream,  as  the  observer 
moves  away  from  it,  are  caused  by  re- 
fraction. The  broken  appearance  of  a 
straight  pole  thrust  obliquely  into 
water  is  accounted  for  by  the  change 

in  direction  which  the  rays  coming  from  the  part  under  water  suffer 
as  they  emerge  into  the  air. 

272.   Cause    of   Refraction.  —  Foucault    in    France    and 

Michelson  in  America 
have  measured  the  veloc- 
ity of  light  in  water,  and 
have  found  that  it  is  only 
three-fourths  as  great  as 
in  air.  The  velocity  of 
light  in  all  transparent 
liquids  and  solids  is  less 
than  in  air,  while  the 
velocity  in  air  is  practi- 
cally the  same  as  in  a 
vacuum. 

If  now  a  beam  of  light 


FIGURE  247.  —  REFRACTION  EXPLAINED. 


240 


LIGHT 


is  incident  obliquely  on  the  surface  MN  of  water  (Fig. 
247),  all  parts  of  a  light  wave  do  not  enter  the  water  at  the 
same  time.  Let  the  parallel  lines  perpendicular  to  AB 
represent  short  portions  of  plane  waves.  Then  one  part 
of  a  wave,  as/,  will  reach  the  water  before  the  other  part, 
as  e,  and  will  travel  less  rapidly  in  the  water  than  in  the 
air.  The  result  is  that  each  wave  is  swung  around,  that 
is,  the  direction  of  propagation  BO,  which  is  perpendicular 
to  the  wave  fronts,  is  changed;  in  other  words,  the  beam 
is  refracted.  The  refraction  of  light  is,  therefore,  due 
to  its  change  in  velocity  in  passing  from  one  transparent 
medium  to  another. 

273.  The  Index  of  Refraction.  — Let  a  beam  of  light  pass 
obliquely  from  air  to  water  or  glass,  and  let  AB  (Fig.  248) 

be  the  incident  wave  front.  From 
A  as  a  center  and  with  a  radius 
AD  equal  to  the  distance  the  light 
travels  in  the  second  medium 
while  it  is  going  from  B  to  0  in 
air,  draw  the  dotted  arc.  This 
limits  the  distance  to  which  the 
disturbance  spreads  in  the  second 
medium.  Then  from  (7  draw  CD 
tangent  to  this  arc  and  draw  AD  to  the  point  of  tangency. 
CD  is  the  new  wave  front. 

The  distances  BC  and  AD  are  traversed  by  the  light  in 
the  same  time.  They  are  therefore  proportional  to  the 
velocities  of  light  in  the  two  media.  Then  the 

T  j        /•     /•      *  •  speed  of  light  in  air          v  1 

Index  of  refraction  =  — r     .     — ^-— — —  =  -: . 

speed  in  second  medium      v 


FIGURE  248.  —  INDEX  OF  RE- 
FRACTION. 


lrThe  older  mathematical  definition  of  the  index  of  refraction  is  the 
ratio  of  the  sine  of  the  angle  of  incidence  to  the  sine  of  the  angle  of  re- 


LAWS   OF  REFRACTION  241 

The  angle  NOB  is  the  angle  of  incidence.  It  is  equal 
to  the  angle  BAG  between  the  incident  wave  front  and 
the  surface  of  separation  of  the  two  media.  The  angle  of 
refraction  is  the  angle  N1 AD.  It  is  equal  to  the  angle 
A  CD  between  the  wave  front  in  the  second  medium  and 
the  surface  of  separation.  The  angle  at  (7,  between  the 
direction  of  the  incident  ray  and  the  refracted  ray,  is  the 
angle  of  deviation. 

The  following  are  the  indices  of  refraction  for  a  few 
substances: 

Water       ....  1.33  Crown  glass         .     .  1.51 

Alcohol     ....  1.36  Flint  glass       1.54  to  1.71 

Carbon  bisulphide      1.64  Diamond    ....  2.47 

For  most  purposes  the  index  of  refraction  for  water  may 
be  taken  as  £ ,  for  crown  glass  £,  for  flint  glass  J^-,  and  for 
diamond  J. 

274.  Laws  of  Refraction.  —  The  following  laws,  which 
summarize  the  facts  relative  to  single  refraction,  were 
discovered  by  Snell,  a  Dutch  physicist,  in  1621: 

I.  When  a  pencil  of  light  passes  obliquely  from  a  less 
highly  to  a  more  highly  refractive  medium,  it  is  bent 
toward  the  normal ;  when  it  passes  in  the  reverse  direc- 
tion, it  is  bent  from  the  normal. 

II.  Whatever  the  angle  of  incidence,  the  index  of  re- 
fraction is  a  constant  for  the  same  two  media. 

fraction.     Now  the  sine  of  an  angle  in  a  right  triangle  is  the  quotient  of 
the  side  opposite  by  the  hypotenuse.    Thus,  the  sine  of  angle  BAG  is 

— ,  and  the  sine  of  ACD  is  45-     Dividing  one  by  the  other,  the  common 

BO     v 
term  AC  cancels  out,  and  the  index  of  refraction  equals  -^  =  -j ,  as  before. 

The  two  definitions  are  therefore  equivalent  to  each  other.     For  the  con- 
struction to  find  the  refracted  ray,  see  the  Appendix. 


242 


LIGHT 


III.    The  planes  of  the  angles  of  incidence  and  refrac- 
tion coincide. 

275.  Refraction  through  Plate  Glass.  —Draw  a  heavy  black 
line  on  a  sheet  of  paper,  and  place  over  it  a  thick  plate  of  glass,  cover- 
ing a  part  of  the  line.     Look  obliquely  through 
the  glass ;  the  line  will  appear  broken  at  the  edge 
of  the  plate,  the  part  under  the  glass  appearing 
laterally  displaced  (Fig.  249). 

To  explain  this,  let  MN  (Fig.  250) 
represent  a  thick  plate  of  glass,  and  AB 
a  ray  of  light  incident  obliquely  upon  it. 
If  the  path  of  the  ray 
be  determined,  the 
emergent  ray  will  be 
parallel  to  the  inci- 
dent ray.  Hence,  the  apparent  position 
of  an  object  viewed  through  a  plate  of 
glass  is  at  one  side  of  its  true  position. 

276.  A  Prism.  —  Let  AB  0  (Fig.  251) 
represent  a  section  of  a  glass  prism 
made  by  a  plane  perpendicular  to  the 
refracting  edge  A.     Also,  let  LI  be  a 


FIGURE  249.  — 
IMAGE  OF  LINE  DIS- 
PLACED. 


FIGURE  250.  —  I  NCI- 
DENT  AND  EMERGENT 
RAYS  PARALLEL. 


ray  incident  on  the  face  BA.  This 
ray  will  be  refracted  along  IE,  and 
entering  the  air  at  the  point  E  will 
be  refracted  again,  taking  the  di- 
rection EO. 

Reflect  across  the  table  a  strong  beam 
of  light  and  intercept  it  with  a  sheet  of 
green  glass.     Let  this  ribbon   of   green 
light  be  incident  on  a  prism  of  small  re- 
fracting angle  in  such  a  manner  that  only  part  of  the  beam  passes 
through  the  prism.     Two  lines  of  light  may  be  traced  through  the 


.Jf 


B  C 

FIGURE  251. —  PATH  OF  LIGHT 
THROUGH  PRISM. 


TOTAL  INTERNAL  REFLECTION 


243 


Horizon 


dust  of  the  room  or  by  means  of  smoke.  By  turning  the  prism  about 
its  axis,  the  angle  between  these  lines  of  light  can  be  varied  in  size. 
It  is  the  angle  of  deviation,  represented  by  the  angle  D  in  the  figure. 
The  angle  of  deviation  is  least  when  the  angles  of  incidence  and 
emergence  are  equal ;  this  occurs  when  the  path  of  the  ray  through 
the  prism  is  equally  inclined  to  the  two  faces. 

277.  Atmospheric  Refraction.  —  Light  coming  to  the  eye 
from  any  heavenly  body,  as  a  star,  unless  it  is  directly 
overhead,     is     gradually       s^ 
bent  as  it  passes  through  \^ 

the  air  on  account  of  the 
increasing  density  of  the 
atmosphere  near  the 
earth's  surface.  Thus,  if 
S  in  Fig.  252  is  the  real 
position  of  a  star,  its  ap- 
parent position  will  be  Sr 
to  an  observer  at  E. 
Such  an  object  appears  higher  above  the  horizon  than  its 
real  altitude.  The  sun  rises  earlier  on  account  of  atmos- 
pheric refraction  than  it  otherwise  would,  and  for  the 
same  reason  it  sets  later.  Twilight,  the  mirage  of  the 

desert,  and  the  looming  of 
distant  objects  are  phenom- 
ena of  atmospheric  refraction. 

278.  Total  Internal  Reflec- 
tion. —  Take  the  apparatus  of  §  271 
and  place  the  cardboard  against  the 
end  of  the  jar  so  that  the  slit  is  near 
the  bottom  (Fig.  253).  Reflect  a 
strong  beam  of  light  up  through 
the  water  and  incident  on  its  under 
surface  just  back  of  the  center  of  the  protractor  scale.  Adjust  the  slit 
so  that  the  beam  shall  be  incident  at  an  angle  a  little  greater  than  50°. 
It  will  be  reflected  back  into  the  water  as  from  a  plane  mirror. 


FIGURE  252.  —  ATMOSPHERIC  REFRACTION. 


FIGURE  253.  —  TOTAL  INTERNAL 
REFLECTION. 


244 


LIGHT 


CRITICAL  ANGLE. 


As  the  angle  of  refraction  is  always  greater  than  the 
angle  of  incidence  when  the  light  passes  from  water  into 
air,  it  is  evident  that  there  is  an  incident  angle  of  such  a 
value  that  the  corresponding  angle  of  refraction  is  90°, 
that  is,  the  refracted  light  is  parallel  to  the  surface.  If 
the  angle  of  incidence  is  still  further  increased,  the  light 

no  longer  passes  out  into 
the  air,  but  suffers  total 
internal  reflection. 

279.  The  Critical  Angle. 
— The  critical  angle  is  the 
angle  of  incidence  corre- 
sponding to  an  angle  of 
refraction  of  90°.  This 
angle  varies  with  the  in- 
dex of  refraction  of  the 
substance.  It  is  about  49°  for  water,  42°  for  crown  glass, 
38°  for  flint  glass,  and  24°  for  diamond. 

Of  all  the  rays  diverging  from  a  point  at  the  bottom 
of  a  pond  and  incident  on  the  surface,  only  those  within 
a  cone  whose  semi-angle  is  49°  pass  into  the  air.  All 
those  incident  at  a  larger  angle  un- 
dergo total  internal  reflection  (Fig. 
254).  Hence,  an  observer  under 
water  sees  all  objects  outside  as  if 
they  were  crowded  into  this  cone ; 
beyond  this  he  sees  by  reflection  ob- 
jects on  the  bottom  of  the  pond. 

Total  reflection  in  glass  is  shown 
by  means  of  a  prism  whose  cross  sec- 
tion is  a  right-angled  isosceles  tri- 
angle (Fig.  255).     A  ray  incident  normally  on  either  face 
about  the  right  angle  enters  the  prism  without  refraction, 


FIGURE  255.  —  TOTAL  RE- 
FLECTION BY  PRISM, 


QUESTIONS  AND  PEOBLEMS  245 

and  is  incident  on  the  hypotenuse  at  an  angle  of  45°, 
which  is  greater  than  the  critical  angle.  The  ray  there- 
fore suffers  total  in- 
ternal reflection  and 
leaves  the  prism  at 
right  angles  to  the  in- 
cident ray.  A  simi-  ______ 

lar  prism  is  sometimes  ^  256.  -  ERECT,NC  PK.SM. 

used  in  a  projecting 

lantern  for  making  the  image  erect  (Fig.  256).     It  would 
otherwise  be  inverted  with  respect  to  the  object. 

Questions  and  Problems 

1.  Why  are  reflectors  back  of  wall  lamps  frequently  made  concave 
at  the  outer  edge  and  convex  in  the  central  part  ? 

2.  Show   that   atmospheric   refraction   increases   the   length   of 
daylight. 

3.  A  plane  mirror  is  revolved  through  an  angle  of  20°.     Show  by 
diagram  that  a  ray  of  light  incident  on  the  mirror  will  be  displaced  40°. 

4.  Show  that  the  deviation  of  a  ray  of  light  by  a  glass  prism  is  in- 
creased by  increasing  the  angle  of  the  prism. 

5.  Show  that  the  deviation  of  a  ray  of  light  by  a  prism  is  increased 
by  increasing  the  index  of  refraction. 

6.  Why  does  the  full  moon  when  seen  near  the  horizon  appear  just 
a  little  elliptical,  the  longer  axis  being  horizontal? 

7.  Why  does  a  stream  of  water,  to  one  standing  on  its  bank,  appear 
less  than  its  true  depth  ? 

8.  A  genuine  diamond  is  distinctly  visible  in  carbon  disulphide,  a 
paste  or  false  diamond  is  nearly  invisible.      Explain.      (The  paste 
diamond  is  flint  glass.) 

9.  What  peculiarity  will  the  image  of  an  object  have  if  the  mirror 
is  convex  cylindrical  ? 

10.  In  spearing  a  fish  from  a  boat  would  you  strike  directly  at  the 
apparent  position  of  the  fish  ?    Explain. 

11.  Show  by  diagram  the  apparent  displacement  of  a  body  as  seen 
by  looking  obliquely  at  it  through  a  plate  glass  window. 


246 


LIGHT 


12.  Why  is  powdered  glass  opaque  ? 

13.  Show  by  diagram  that  a  triangular  prism  of  air  within  water 
has  the  opposite  effect  on  the  direction  of  a  ray  of  light  passing  through 
it  that  a  prism  of  water  in  air  has. 

V.    LENSES 

280.  Kinds  of  Lenses.  — A  lens  is  a  portion  of  a  transpar- 
ent substance  bounded  by  two  surfaces,  one  or  both  being 


FIGURE  257.  —  FORMS  OF  LENSES. 


curved.     The  curved  surfaces  are  usually  spherical  (Fig. 
257).     Lenses  are  classified  as  follows: 


1.  Double-convex,  —  both  surfaces  convex     .     . 

2.  Plano-convex,  —  one     surface     convex,     one 

plane • 

3.  Concavo-convex,  —  one   surface  convex,   one 

concave 

4.  Double-concave,  —  both  surfaces  concave  .     . 

5.  Plano-concave,  —  one    surface    concave,    one 

plane 

6.  Convexo-concave,  —  one  surface  concave,  one 

convex     .          


Converging  lenses, 
thicker  at  the  middle 
than  at  the  edges. 


Diverging  lenses, 

thinner  at  the  middle 

than  at  the  edges. 


TRACING  BAYS.  THROUGH  LENSES 


247 


The  concavo-convex  and  the  convexo-concave  lenses 
are  frequently  called  meniscus  lenses.  The  double-con- 
vex lens  may  be  regarded  as  the  type  of  the  converging 
class  of  lenses,  and  the  double-concave  lens  of  the  diverg- 
ing class. 

281.  Definition  of  Terms  relating  to  Lenses.  —  The  centers 
of  the  spherical  surfaces  bounding  a  lens  are  the  centers  of 
curvature.  The  optical  center  is  a  point  such  that  any  ray 
passing  through  it  and  the  lens  suffers  no  change  of  di- 
rection. In  lenses  whose 
surfaces  are  of  equal  curv-  ^x^  x\/'' 
ature,  the  optical  center 
is  their  center  of  volume, 
as  0,  in  Fig.  258.  In 
piano-lenses,  the  optical 
center  is  the  middle  point 
of  the  curved  face.  The 
straight  line,  <7CV,  through  the  centers  of  curvature,  is  the 
principal  axis,  and  any  other  straight  line  through  the  op- 
tical center,  as  EH,  is  a  secondary  axis.  The  normal  at 
any  point  of  the  surface  is  the  radius  of  the  sphere  drawn 


FIGURE  238.  —  OPTICAL  CENTER  OF  LENS. 


FIGURE  259.  —  TRACING  RAY  THROUGH  CONVERGING  LENS. 

to  that  point ;   thus  CD  is  the  normal  to  the  surface  AnB 
at  D. 

282.   Tracing  Rays  through  Lenses.  —  A   study  of  Figs. 
259  and  260  shows  that  the  action  of  lenses  on  rays  of 


248  LIGHT 

light  traversing  them  is  similar  to  that  of  prisms,  and 
conforms  to  the  principle  illustrated  in  §  276.  A  ray  is 
always  refracted  toward  the  perpendicular  on  entering  a 
denser  medium  (glass)  and  away  from  it  on  entering  a 
medium  of  less  optical  density.  Thus  we  see  that  the 
convex  lens  bends  a  ray  toward  the  principal  axis,  while 
the  concave  lens  (Fig.  260)  bends  it  away  from  this  axis. 


N 
FIGURE  260.  —  TRACING  RAY  THROUGH  DIVERGING  LENS. 

(For  tracing  the  path  of  a  ray  geometrically,  consult 
Appendix  V.) 

283.  The  Principal  FOCUS.  —  Hold  a  converging  lens  so  that  the 
rays  of  the  sun  fall  on  it  parallel  to  its  principal  axis.  Beyond  the 
lens  hold  a  sheet  of  white  paper,  moving  it  until  the  round  spot  of 
light  is  smallest  and  brightest.  If  held  steadily,  a  hole  may  be 
burned  through  the  paper.  This  spot  marks  the  principal  focus  of 
the  lens,  and  its  distance  from  the  optical  center  is  the  principal  focal 
length. 

For  double-convex  lenses,  the  two  faces  having  the 
same  radius  of  curvature,  the  principal  focus  is  at  the 
center  of  curvature  when  the  index  of  refraction  is  1.5. 
If  the  index  is  greater  than  1.5,  the  focal  length  is  less 
than  the  radius  of  curvature ;  if  less  than  1.5,  it  is 
greater  than  this  radius. 

Converging  lenses  are  sometimes  called  burning  glasses 
because  of  their  power  to  focus  the  heat  rays,  as  shown  in 
the  experiment. 


CONJUGATE  FOCI  OF  LENSES 


249 


Figure  261  shows  that  parallel  rays  are  made  to  con- 
verge toward  the  principal  focus  .Fby  a  converging  lens, 
and  the  focus  is 
real;  on  the  other 
hand,  Fig.  262  illus-  A 
trates  the  diverging 
effect  of  a  concave 
lens  on  parallel  rays; 
the  focus  F  is  now 
virtual  because  the  FIGURE  261.  —  PRINCIPAL  Focus  OF  A 

rays    after    passing 

through  the  lens  only  apparently  come  from  F.  In  gen- 
eral, converging  lenses  increase  the  convergence  of  light, 
while  diverging  lenses  decrease  it. 


FIGURE  262.  —  PRINCIPAL  Focus  OF  A  DIVERGING  LENS. 

284.  Conjugate  Foci  of  Lenses.  —  If  a  pencil  of  light  di- 
verges from  a  point  and  is  incident  on  the  lens,  it  is 
focused  at  a  point  on  the  axis  through  the  radiant  point. 


FIGURE  263.  —  CONJUGATE  Foci,  CONVERGING  LENS. 


250  LIGHT 

These  points  are  called  conjugate  foci,  for  the  same  reason 
as  in  mirrors. 

In  Fig.  263  a  pencil  of  rays  BAE  diverges  from  A  and 
is  focused  by  the  lens  at  the  point  H.  It  is  evident  that 
if  the  rays  diverge  from  H,  they  would  be  brought  to  a 
focus  at  A.  Hence  A  and  H  are  conjugate  foci. 

285.  Images  by  Lenses.  —  Place  in  a  line  on  the  table  in  a  dark- 
ened room  a  lamp,  a  converging  lens  of  known  focal  length,  and  a 
white  screen.  If,  for  example,  the  focal  length  of  the  lens  is  30  cm., 
place  the  lamp  about  70  cm.  from  it,  or  more  than  twice  the  focal 
length,  and  move  the  screen  until  a  clearly  denned  image  of  the  lamp 
appears  on  it.  This  image  will  be  inverted,  smaller  than  the  object, 
and  situated  between  30  cm.  and  60  cm.  from  the  lens.  By  placing 
the  lamp  successively  at  60  cm.,  50  cm.,  30  cm.,  and  20  cm.,  the  images 
will  differ  in  position  and  size,  and  in  the  last  case  will  not  be  received 
on  the  screen,  but  may  be  seen  by  looking  through  the  lens  toward 
the  lamp.  If  a  diverging  lens  be  used,  no  image  can  be  received  on 
the  screen  because  they  are  all  virtual. 

The  results  of  such  an  experiment  may  be  summarized 
as  follows  : 

I.  When  the  object  is  at  a  finite  distance  from  a  con- 
verging lens,  and  farther  than  twice  the  focal  length,  the 


N 
FIGURE  264.  —  OBJECT  FARTHER  THAN  TWICE  FOCAL  LENGTH  FROM  LENS. 

image  is  real,  inverted,  at  a  distance  from  the  lens  of 
more  than  once  and  less  than  twice  the  focal  length,  and 
smaller  thanrthe  object  (Fig.  264).. 


IMAGES  BY  LENSES 


251 


IT.    When  the  object  is  at  a  distance  of  twice  the  focal 
length  from  a  converging  lens,  the  image  is  real,  inverted, 


FIGURE  265.  —  OBJECT  TWICE  FOCAL  LENGTH  FROM  LENS° 

at  the  same  distance  from  the  lens  as  the  object,  and  of 
the  same  size  (Fig.  265). 

III.    When   the    object  is  at  a  distance   from   a   con- 
verging lens  of  less  than  twice  and  more  than  once  its 


FIGURE  266.  —  OBJECT  LESS  THAN  TWICE  FOCAL  LENGTH  FROM  LENS. 

focal  length,  the  image  is  real,  inverted,  at  a  distance  of 
more  than  twice  the  focal  length,  and  larger  than  the 
object  (Fig.  266). 

IV.  When  the  object  is  at  the  principal  focus  of  a  con 
verging  lens,  no  distinct  image  is  formed  (Fig.  267). 


FIGURE  267.  —  OBJECT  AT  PRINCIPAL  Focus. 


252 


LIGHT 


V.  When  the  object  is  between  a  converging  lens  and 
its  principal  focus,  the  image  is  virtual,  erect,  and  en- 
larged (Fig.  268). 


FIGURE  268.  —  OBJECT  LESS  THAN  FOCAL  LENGTH  FROM  LENS. 

VI.  With  a  diverging  lens,  the  image  is  always  virtual, 
erect,  and  smaller  than  the  object  (Fig.  269). 

286.  Graphic  Construction  of  Images  by  Lenses.  —  The  im- 
age of  an  object  by  a  lens  consists  of  the  images  of  its 
points.  If  the  object  is  represented  by  an  arrow,  it  is 


FIGURE  269.  —  IMAGE  VIRTUAL  IN  DIVERGING  LENS. 


This 


necessary  to  find  only  the  images  of  its  extremities, 
is  readily  done  by  following  two  general  directions: 

First.  Draw  secondary  axes  through  the  ends  of  the 
arrow.  These  represent  rays  that  suffer  no  change  in 
direction  because  they  pass  through  the  optical  center 
(§  281). 

Second.  Through  the  ends  of  the  arrow  draw  rays 
parallel  to  the  principal  axis.  After  leaving  the  lens, 
these  pass  through  the  principal  focus  (§  283). 


SPHERICAL  ABERRATION  IN  LENSES  253 

The  intersection  of  the  two  refracted  rays  from  each 
extremity  will  be  its  image. 

To  illustrate.  Let  AS  be  the  object  and  MN  the  lens 
(Figs.  264-269).  Rays  along  secondary  axes  through  0 
pass  through  the  lens  without  any  change  in  direction. 
The  rays  AD  and  BH,  parallel  to  the  principal  axis,  are 
refracted  in  the  lens  along  DE  and  HI  respectively,  and 
emerge  from  the  lens  in  a  direction  which  passes  through 
the  principal  focus  F.  The  intersection  of  Aa  with  Ea 
is  the  image  of  A,  and  that  of  Bb  with  Ib  is  the  image  of 
B.  Other  rays  from  A  and  B  also  pass  through  a  and  b 
respectively,  and  therefore  ab  is  the  image  of  AB.  The 
image  is  virtual  when  the  intersection  of  the  refracted 
rays  is  on  the  same  side  of  the  lens  as  the  object.  The 
relative  size  of  object  and  image  is  the  same  as  their  rela- 
tive distance  from  the  lens. 

287.  Spherical  Aberration  in  Lenses.  —  If  rays  from  any 
point  be  drawn  to  different  parts  of  a  lens,  and  their 


FIGURE  270.  —  SPHERICAL  ABERRATION. 

directions  be  determined  after  refraction,  it  will  be  found 
that  those  incident  near  the  edge  of  the  lens  cross  the 
principal  axis,  after  emerging,  nearer  the  lens  than  those 
incident  near  the  middle  (Fig.  270).  The  principal  focal 
length  for  the  marginal  rays  is  therefore  less  than  for 
central  rays.  This  indefiniteness  of  focus  is  called  spherical 
aberration  by  refraction,  the  effect  of  which  is  to  lessen  the 


254  LIGHT 

distinctness  of  images  formed  by  the  lens.  In  practice  a 
round  screen,  called  a  diaphragm,  is  used  to  cut  off  the 
marginal  rays  ;  this  renders  the  image  sharper  in  outline, 
but  less  bright.  In  the  large  lenses  used  in  telescopes  the 
curvature  of  the  lens  is  made  less  toward  the  edge,  so  that 
all  parallel  rays  are  brought  to  the  same  focus. 

288.   Formula  for  Lenses.  — The  triangles  AOK  and  aOL  in 

Fig.  271  are  similar.  Hence,  —j-  =  -j—r  •  If  the  lens  is  thin,  a  straight 
line  connecting  D  and  H  will  pass  very  nearly  through  the  optical 

A 


FIGURE  271.  —  RELATION  BETWEEN  OBJECT  AND  IMAGE. 

center  0.     Then  DFO  is  a  triangle  similar  to  aFL,  and  —  =  —  . 

a,L      LF 

Since  DO  is  equal  to  AK,  the  first  members  of  the  two  equations 
above  are  equal  to  each  other,  and  therefore 
LO  -  q,  and  OF  =/.     Then  LF  =  q  -/,  and 


K^O      OF 

above  are  equal  to  each  other,  and  therefore  —  =  --     Put  KO  =p, 

LO     LF 


Clearing  of  fractions  and  dividing  through  by  pqf,  we  have 

1  =  1  +  1  ......   (Equation  32) 

/    P      q 

By  measuring  p  and  q  we  may  compute  /.     For  diverging  lenses 
/and  q  are  negative. 

Questions  and  Problems 

1.  How  can  a  convex  lens  be  distinguished  from  a  concave  one  ? 

2.  Why  does  common  window  glass  often  give  distorted  images  of 
objects  viewed  through  it? 


THE  MAGNIFYING   GLASS  255 

3.  How  can  the  principal  focal  length  of  a  concave  spherical  mirror 
be  found  ? 

4.  Given  a  collection  of  spectacle  lenses ;  select  the  concave  from 
the  convex. 

5.  Why  do  so  many  cheap  mirrors  give  distorted  images  ? 

6.  If  an  oarsman  sticks  his  oar  into  the  water  obliquely,  why  does 
it  appear  broken  at  the  point  of  entrance  ? 

7.  Concave  spherical  mirrors  are  often  mounted  in  frames  to  be 
used  as  hand  glasses.     Such  mirrors  are  usually  made  by  silvering  one 
face  of  a  lens.     Why  can  several  images  be  seen  in  such  a  mirror? 

8.  When  is  the  distance  between  the  object  and  its  real  image  as 
formed  by  a  converging  lens  the  least  possible? 

9.  The  focal  length  of  a  camera  lens  is  two  inches.     How  far  must 
the  sensitized  plate  be  from  the  lens,  when  the  object  is  distant  100  ft.  ? 

10.  If  a  reading  glass  has  a  focal  length  of  16  in.  and  in  its  use  is 
held  10  in.  from  the  book,  what  is  the  position  of  the  virtual  image? 

11.  An  object  100  cm.  in  front  of  a  converging  lens  gives  an  image 
25  cm.  back  of  the  lens.     What  is  the  focal  length  of  the  lens? 

12.  Show  by  diagram  what  effect  it  has  on  the  image  of  an  object 
by  a  diverging  lens  to  move  it  farther  away  from  the  lens. 

13.  Why  is  a  convex  mirror  used  on  an  automobile  to  view  objects 
back  of  the  driver,  instead  of  a  plane  mirror  ? 

14.  In  a  diverging  lens,  show  that  a  pencil  of  light  that  converges 
to  a  point  beyond  the  focus  of  the  lens  issues  as  a  diverging  pencil. 

15.  Where  must  a  diverging  lens  be  placed  to  render  parallel  a 
converging  pencil  of  light? 

VI.   OPTICAL  INSTRUMENTS 

289.  The  Magnifying  Glass,  or  simple  microscope,  is  a 
double-convex  lens,  usually  of  short  focal  length.  The 
object  must  be  placed  nearer  the  lens  than  its  principal 
focus.  The  image  is  then  virtual,  erect,  and  enlarged. 
If  AB  is  the  object  in  Fig.  272,  the  virtual  image  is  ab  ; 
and  if  the  eye  be  placed  near  the  lens  on  the  side  opposite 


256 


LIGHT 


the  object  the  virtual  image  will  be  seen  in  the  position  of 
the  intersection  of  the  rays  produced,  as  at  ab. 


FIGURE  272.  —  MAGNIFYING  GLASS. 

290.  The  Compound  Microscope  (Fig.  273)  is  an  instru- 
ment designed  to  obtain  a  greatly  enlarged  image  of  very 
small  objects.  In  its  simplest  form  it  consists  of  a  con- 
verging lens  JOT  (Fig.  274), 
called  the  object  glass  or  ob- 
jective, and  another  con- 
verging lens  RS,  called  the 
eye-piece.  The  two  lenses 
are  mounted  in  the  ends  of 
the  tube  of  Fig.  273.  The 
object  is  placed  on  the  stage 
just  under  the  objective,  and 
•  a  little  beyond  its  principal 
focus.  A  real  image  ab 
(Fig.  274)  is  formed  slightly 
nearer  the  eye-piece  than  its 
focal  length.  This  image 
formed  by  the  objective  is 

FIGURE  273.  -  MICROSCOPE.  viewed  b?  the  eyepiece,  and 

the  latter  gives  an  enlarged 

virtual   image.     (Why?)     Both   the   objective   and   the 
eyepiece  produce  magnification. 


THE  ASTRONOMICAL    TELESCOPE 


257 


291.  The  Astronomical  Telescope.  — The  system  of  lenses 
in  the  refracting  astronomical  telescope  (Fig.  275)  is  simi- 
lar to  that  of  the  compound  microscope.  Since  it  is  in- 
tended to  view  distant  objects,  the  objective  MN  is  of 


FIGURE  274.  —  TRACING  RAYS  TO  FORM  IMAGE 

large  aperture  and  long  focal  length.  The  real  image 
given  by  it  is  the  object  for  the  eyepiece,  which  again 
forms  a  virtual  image  for  the  eye  of  the  observer.  The 
magnification  is  the  ratio  of  the  focal  lengths  of  the  objec- 
tive and  the  eyepiece.  The  objective  must  be  large,  for 
the  purpose  of  collecting  enough  light  to  permit  large 


or          A^ 

FIGURE  275.  —  IMAGE  IN  ASTRONOMICAL  TELESCOPE. 

magnification   of    the   image   without   too   great   loss   in 
brightness. 

Figure  275  shows  that  the  image  in  the  astronomical 
telescope  is  inverted.  In  a  terrestrial  telescope  the  image 
is  made  erect  by  introducing  near  the  eyepiece  two  double- 
convex  lenses,  in  such  relation  to  each  other  and  to  the 
first  image  that  a  second  real  image  is  formed  like  the  first, 
but  erect. 


258 


LIGHT 


292.  Galileo's  Telescope.  —  The  earliest  form  of  telescope 
was  invented  by  Galileo.  It  produces  an  erect  image  by 
the  use  of  a  diverging  lens  for  the  eyepiece  (Fig.  276). 
This  lens  is  placed  between  the  objective  and  the  real 
image,  ab,  which  would  be  formed  by  the  objective  if  the 
eyepiece  were  not  interposed.  Its  focus  is  practically  at 
the  image  ab,  and  the  rays  of  light  issue  from  it  slightly 


FIGURE  276.  —  GALILEO'S  TELESCOPE. 

divergent  for  distant  objects.  The  image  is  therefore  at 
A1 B1  instead  of  at  ab,  and  it  is  erect  and  enlarged.  This 
telescope  is  much  shorter  than  the  astronomical  telescope, 
for  the  distance  between  the  lenses  is  the  difference  of 
their  focal  lengths  instead  of  their  sum.  In  the  opera 
glass  two  of  Galileo's  telescopes  are  attached  together 
with  their  axes  parallel. 

293.  The  Projection  Lantern  is  an  apparatus  by  which  a 
greatly  enlarged  image  of  an  object  can  be  projected  on  a 
screen.  The  three  essentials  of  a  projection  lantern  are 
a  strong  light,  a  condenser,  and  an  objective.  The  light 
may  be  the  electric  arc  light,  as  shown  in  Fig.  277,  the 
calcium  light,  or  a  large  oil  burner.  The  condenser  E  is 
composed  of  a  pair  of  converging  lenses;  its  chief  pur- 
pose is  the  collection  of  the  light  on  the  object  by  refrac- 
tion, so  as  to  bring  as  much  as  possible  on  the  screen. 
The  object  AB,  commonly  a  drawing  or  a  photograph 


:m- 


MOVING  PICTURE  FILM. 
Most  moving  picture  cameras  take  from  16  to  120  pictures  per  second. 


THE  EYE 


259 


on  glass,  is  placed  near  the  condenser  SS,  where  it  is 
strongly  illuminated.  The  objective,  MN,  is  a  combina- 
tion of  lenses,  acting  as  a  single  lens  to  project  on  the 
screen  a  real,  inverted,  and  enlarged  image  of  the  object. 


FIGURE  277.  —  PROJECTION  LANTERN. 

294.  The  Photographer's  Camera  consists  of  a  box  BQ 
(Fig.  278),  adjustable  in  length,  blackened  inside,  and 
provided  at  one  end  with  a  lens  or  a  combination  of  lenses, 
acting  as  a  single  one,  and  at  the  other  with  a  holder  for 
the  sensitized  plate.     If  by  means  of  a  rack  and  pinion  the 
lens  U  be  properly 

focused  for  an  ob- 
ject in  front  of  it, 
an  inverted  image 
will  be  formed  on 
the  sensitized  plate 
E.  The  light  acts 
on  the  salts  con- 
tained in  the  sensitized  film,  producing  in  them  a  modifi- 
cation which,  by  the  processes  of  "developing"  and  "fix- 
ing," becomes  a  permanent  negative  picture  of  the  object. 
When  a  "  print "  is  made  from  this  negative,  the  result  is 
a  positive  picture. 

295.  The  Eye. — The  eye  is  like  a  small  photographic 
camera,  with  a  converging  lens,  a  dark  chamber,  and  a 


FIGURE  278.  —  CAMERA. 


260 


LIGHT 


FIGURE  279.  —  SECTION  OF  EYE. 


sensitive  screen.  Figure  279  is  a  vertical  section  through 
the  axis.  The  outer  covering,  or  sclerotic  coat  H,  is  a 
thick  opaque  substance,  except  in  front,  where  it  is  ex- 
tended as  a  transparent  coat,  called  the  cornea  A.  Behind 

the  cornea  is  a  dia- 
phragm D,  consti- 
tuting the  colored 
part  of  the  eye,  or 
the  iris.  The  cir- 
cular opening  in  the 
iris  is  the  pupil, 
the  size  of  which 
changes  with  the 
intensity  of  light. 
Supported  from  the 
walls  of  the  eye, 
just  back  of  the  iris,  is  the  crystalline  lens  E,  a  transparent 
body  dividing  the  eye  into  two  chambers;  the  anterior 
chamber  between  the  cornea  and  the  crystalline  lens  is  a 
transparent  fluid  called  the  aqueous  humor,  while  the  large 
chamber  behind  the  lens  is  filled  with  a  jellylike  substance 
called  the  vitreous  humor.  The  choroid  coat  lines  the  walls 
of  this  posterior  chamber,  and  on  it  is  spread  the  retina,  a 
membrane  traversed  by  a  network  of  nerves,  branching 
from  the  optic  nerve  M.  The  choroid  coat  is  filled  with  a 
black  pigment,  which  serves  to  darken  the  cavity  of  the 
eye,  and  to  absorb  the  light  reflected  internally. 

296.  Sight.  —  When  rays  of  light  diverge  from  the  ob- 
ject and  enter  the  pupil  of  the  eye  they  form  an  inverted 
image  on  the  retina  (Fig.  280)  precisely  as  in  the  photo- 
graphic camera.  In  place  of  the  sensitized  plate  is  the 
sensitive  retina,  from  which  the  stimulus  is  carried  to  the 
brain  along  the  optic  nerve. 


THE  BLIND   SPOT  261 

In  the  camera  the  distance  between  the  lens  and  the 
screen  or  plate  must  be  adjusted  for  objects  at  different 
distances.  In  the  eye  the  corresponding  distance  is  fixed, 
and  the  adjustment  for  distinct  vision  is  made  by  uncon- 
sciously changing  the  curvature  of  the  front  surface  of 


FIGURE  280.  —  IMAGE  ON  RETINA. 

the  crystalline  lens  by  means  of  the  ciliary  muscle  JF,  Gr 
(Fig.  279).  This  capability  of  the  lens  of  the  eye  to 
change  its  focal  length  for  objects  at  different  distances 
is  called  accommodation. 

297.  The  Blind  Spot. — There  is  a  small  depression  where 
the  optic  nerve  enters  the  eye.  The  rest  of  the  retina  is 
covered  with  microscopic  rods  and  cones,  but  there  are 
none  in  this  depression,  and  it  is  insensible  to  light.  It  is 


FIGURE  281.  —  To  FIND  BLIND  SPOT. 

accordingly  called  the  blind  spot.  Its  existence  can  be 
readily  proved  by  the  help  of  Fig.  281.  Hold  the  book 
with  the  circle  opposite  the  right  eye.  Now  close  the  left 
eye  and  turn  the  right  to  look  at  the  cross.  Move  the 
book  toward  the  eye  from  a  distance  of  about  a  foot,  and 
a  position  will  readily  be  found  where  the  black  circle 
will  disappear.  Its  image  then  falls  on  the  blind  spot. 
It  may  be  brought  into  view  again  by  moving  the  book 
either  nearer  the  eye  or  farther  away. 


262  LIGHT 

298.  The    Prism    Binocular.  -  -  While    the    opera    glass 
(§  292)  is  compact  and  gives  an  erect  image,  it  has  only 
a  small  field  of  view,  and  is  usually  made  to  magnify  only 
three   or   four   times.      For   the   purpose  of  obtaining   a 
larger  field  of  view   with  equal  compactness,  the  prism 

binocular  has  been  devised. 
The  desired  length  has  been 
obtained  by  the  use  of  two 
total  reflecting  prisms  (Fig. 
282),  by  means  of  which 
the  light  is  reflected  forward 
and  back  again  in  the  tube. 
Not  only  is  compactness 

secured  in  this  manner,  but 
FIGURE  282.  —  PRISM  BINOCULAR.  .          . 

the  reflections  in  the  prisms 

increase  the  focal  length  of  the  objective  and  serve  to  give 
an  erect  image  without  "  perversion." 

299.  Defects  of  the  Eye.  —  A  normal  eye  in  its  passive  or 
relaxed  condition  focuses  parallel  rays  on  the  retina.     The 
defects  of  most  frequent  occurrence  are  near-sightedness, 
far-sightedness,  and  astigmatism. 

If  the  relaxed  eye  focuses  parallel  rays  in  front  of  the 
retina  (Fig.  283),  it  is  near-sighted.  The  length  of  the 
eyeball  from  front  to  back 
is  then  too  great  for  the 
focal  length  of  the  crys- 
talline lens.  The  correc- 
tion consists  in  placing  in 
/.  £  ,-,  -,.  FIGURE  283.  —  NEAR-SIGHTEDNESS. 

iront  ot  the  eye  a  diverg- 
ing lens  that  makes  with  the  lens  of  the  eye  a  less  con- 
vergent system  than  the  crystalline   lens  itself.     If   the 
focal  length  of  the  diverging  lens  is  equal  to  the  greatest 
distance  of  distinct  vision  for  the  near-sighted  eye,  and  if 


ANALYSIS   OF  WHITE  LIGHT  263 

this  lens  is  held  close  to  the  eye,  parallel  rays  from  a  dis- 
tant object  will  enter  the  eye  as  if  they  came  from  the 
principal  focus  of  the  lens,  the  image  falls  on  the  retina, 
and  vision  is  made  distinct. 

If  the  relaxed  eye  focuses  parallel  rays  from  distant 
objects  behind  the  retina,  it  is  far-sighted.  The  length  of 
the  eyeball  is  then  too  short  to  correspond  with  the  focal 
length  of  the  crystalline 
lens.  The  correction  con- 
sists  in  placing  in  front  of 
the  eye  a  converging  lens 

(Fig.    284),   making  with 

FIGURE  284.  — FAR-SIGHTEDNESS. 
the  lens  of  the  eye  a  more 

converging  system  than  the  eye  lens  alone.  Light  from 
a  near  object  then  enters  the  eye  as  if  it  came  from  a  dis- 
tant one  and  vision  becomes  distinct. 

Sometimes  the  front  of  the  cornea  has  different  curva- 
tures in  different  planes  through  the  axis ;  that  is,  it  has 
a  somewhat  cylindrical  form.  Persons  with  such  an  eye 
do  not  see  with  equal  distinctness  all  the  figures  on  the 
face  of  a  watch.  This  defect  is  known  as  astigmatism. 
Tt  is  corrected  by  the  use  of  a  lens,  one  surface  of  which 
at  least  is  not  spherical  but  differs  from  it  in  the  opposite 
sense  to  that  of  the  defective  eye.  The  astigmatism  of 
the  two  eyes  is  not  usually  the  same. 

VII.   DISPERSION 

300.   Analysis  of   White   Light.      The  Solar  Spectrum.— 

Darken  the  room,  and  by  means  of  a  mirror  hinged  outside  the  window, 
reflect  a  pencil  of  sunlight  into  the  room.  Close  the  opening  in  the 
window  with  a  piece  of  tin,  in  which  is  cut  a  very  narrow  vertical  slit. 
Let  the  ribbon  of  sunlight  issuing  from  the  slit  be  incident  obliquely 
on  a  glass  prism  (Fig.  285).  A  many-colored  band,  gradually  chang- 
ing from  red  at  one  end  through  orange,  yellow,  green,  blue,  to  violet 


264 


LIGHT 


at  the  other,  appears  on  the  screen.  If  a  converging  lens  of  about  30 
cm.  focal  length  be  used  to  focus  an  image  of  the  slit  on  the  screen, 
and  the  prism  be  placed  near  the  principal  focus,  the  colored  images 

, of    the   slit  will  be 

more  distinct. 

This  experi- 
ment shows  that 
white  or  colorless 
light  is  a  mix- 
ture of  an  infinite 
number  of  differ- 
ently colored 
rays,  of  which 
the  red  is  re- 
fracted least  and 
the  violet  most. 
The  brilliant  band  of  light  consists  of  an  indefinite  num- 
ber of  colored  images  of  the  slit ;  it  is  called  the  solar 
spectrum,  and  the  opening  out  or  separating  of  the  beam 
of  white  light  is  known  as  dispersion. 

301.  Synthesis  of  Light.  — Project  a  spectrum  of  sunlight  on  the 
screen.  Now  place  a  second  prism  like  the  first  behind  it,  but  re- 
versed in  position  (Fig.  286).  There 
will  be  formed  a  colorless  image, 
slightly  displaced  on  the  screen. 


FIGURE. 285.  —  ANALYSIS  OF  WHITE  LIGHT. 


FIGURE  286.  —  REFORMING 
WHITE  LIGHT. 


The  second  prism  reunites  the 
colored  rays,  making  the  effect 
that  of  a  thick  plate  of  glass  (§  275).  The  recomposition 
of  the  colored  rays  into  white  light  may  also  be  effected  by 
receiving  them  on  a  concave  mirror  or  a  large  convex  lens. 

302.   Chromatic  Aberration.  —  Let  a  beam  of  sunlight  into  the 
darkened  room  through  a  round  hole  in  a  piece  of  cardboard.     Pro- 


THE  ACHROMATIC  LENS 


265 


ject  an  image  of  this  aperture  on  the  screen,  using  a  double-convex 
lens  for  the  purpose.  The  round  image  will  be  bordered  with  the 
spectral  colors. 

This  experiment  shows  that  the  lens  refracts  the  rays 

of  different  colors  to  different  foci.  This  defect  in  lenses 
is  known  as  chromatic  aberration. 

The  violet   rays,   being  more   re-     s 

frangible  than  the  red,  will  have  > 

their  focus  nearer  to  the  lens  than     5 

the   red,  as   shown   in   Fig.    287, 

where  v  is  the  principal  focus  for     FlGURE  A287-  ~  CHROMATIC 

T  i        f  TP  ABERRATION. 

violet  light  and  r  for  red.     If   a 

screen  were  placed  at  x,  the  image  would  be  bordered 
with  red,  and  if  at  y  with  violet. 

303.  The  Achromatic  Lens.  — With  a  prism  of  crown  glass  pro- 
ject a  spectrum  of  sunlight  on  the  screen,  and  note  the  length  of  the 
spectrum  when  the  prism  is  turned  to  give  the  least  deviation  (§  276). 
Repeat  the  experiment  with  a  prism  of  flint  glass  having  the  same  re- 
fracting angle.  The  spectrum  formed  by  the  flint  glass  will  be  about 
twice  as  long  as  that  given  by  crown  glass,  while  the  position  of  the 
middle  of  the  spectrum  on  the  screen  is  about  the  same  in  the  two 
cases.  Now  use  a  flint  glass  prism  whose  refracting  angle  is  half  that 
of  the  crown  glass  one.  The  spectrum  is  nearly  equal  in  length  to 

^^  that  given  by  the  crown 
glass -prism,  but  the  devia- 
tion  of  the  middle  of  it  is 
considerably  less.  Finally, 
place  this  flint  glass  prism 
in  a  reversed  position 

against  the  crown  glass  one 
FIGURE  288.  —  ACHROMATIC  PRISM.  "5,.     nnn^      _, 

(Fig.  288).     The  image  of 

the  aperture  is  no  longer  colored,  arid  the  deviation  is  about  half  that 
produced  by  the  crown  glass  alone. 

In  1757  Dollond,  an  English  optician,  combined  a  double- 
convex  lens  of  crown  glass  with  a  plano-concave  lens  of 


266 


LIGHT 


flint  glass  so  that  the  dispersion  by  the  one  neutralized 
that  due  to  the  other,  while  the  refraction  was  reduced 
about  half  (Fig.  289).  Such  a  lens  or  system 
of  lenses  is  called  achromatic,  since  images 
formed  by  it  are  not  fringed  with  the  spectral 
colors. 

304.    The  Rainbow. — Cement  a  crystallizing  beaker 
FIGURE  289.    12  or  15  cm.  in  diameter  to  a  slate  slab.     Fill  the  beaker 

With  Water  throu£n  a  hole  drilled  in  the  slate-  SaP- 
port  the  slate  in  a  vertical  plane  and  direct  a  ribbon 
of  white  light  upon  the  beaker  at  a  point  about  60°  above  its  hori- 
zontal axis,  as  SA  (Fig.  290).  The  light  may  be  traced  through  the 
water,  part  of  it  issuing  at  the  back  at  B  as  a  diverging  pencil,  and 
a  part  reflected  to  C  and  issuing  as  spectrum  colors  along  CD.  If 
other  points  of  incidence  be  tried,  the  colors  given  by  the  reflected 
portion  are  very  indistinct  except  at  70°  below  the  axis.  After  re- 
fraction at  this  point, 
the  light  can  be  traced 
through  the  water,  is- 
suing as  spectral  colors 
after  having  suffered 
two  refractions  and 
two  reflections. 


7 


FIGURE  290.  —  ILLUSTRATING  RAINBOW. 


The  experiment 
shows  that  the  light 
must  be  incident  at 
definite  angles  to 
give  color  effects.  The  red  constituent  of  white  light  in- 
cident at  about  60°  keeps  together  after  reflection  and 
subsequent  refraction ;  that  is,  the  red  rays  are  practically 
parallel  and  thus  have  sufficient  intensity  to  produce  a 
red  image.  The  same  is  true  of  the  violet  light  incident 
at  about  59°  from  the  axis.  The  other  spectral  colors  ar- 
range themselves  in  order  between  the  red  and  violet. 

For  light  incident  at  about  70°  from  the  axis  a  similar 


DISCONTINUOUS   SPECTRA 


267 


ct  _ 


FlGURE  »>--P™AWAHD  SECONDARY  Bows. 


spectrum  band  is  formed  by  light  which  has  suffered  two 
refractions  and  two  reflections. 

So  when  sunlight  falls  on  raindrops  the  light  is  dispersed 
and  a  rainbow  is  formed.  Two  bows  are  often  visible,  the 
primary  and  the  secondary.  The  primary  is  the  inner  and 
brighter  one,  formed  by  a  single  internal  reflection.  It  is 
distinguished  by  hav- 
ing the  red  on  the  out- 
side and  the  violet  on 
the  inside.  The  sec- 
ondary bow,  formed 
by  two  internal  reflec- 
tions, is  fainter,  and 
has  the  order  of  colors 
reversed.  Figure  291 
shows  the  relative  po- 
sitions  of  the  sun,  the  observer,  and  the  raindrops  which 
form  the  bows.  It  should  be  noted  that  all  drops  in  the 
line  vE  send  violet  light  to  the  eye,  those  along  rE  send 
red  light,  and  those  between  the  two  send  the  intermediate 
colors. 

305.  Continuous  Spectra.  —  Throw  on  a  screen  the  spectrum  of 
the  electric  arc,  using  preferably  for  the  purpose  a  hollow  prism  filled 
with  carbon  bisulphide.      The  spectrum  will  be  composed  of  colors 
from  red  at  one  end  through  orange,  yellow,  green,  blue,  and  violet 
at  the  other  without  interruptions  or  gaps. 

The  experiment  illustrates  continuous  spectra,  that  is, 
spectra  without  breaks  or  gaps  in  the  color  band.  Solids, 
liquids,  and  dense  vapors  and  gases,  when  heated  to  incan- 
descence, give  continuous  spectra. 

306.  Discontinuous  SpeQtra.  —  Project  on  the  screen  the  spectrum 
of  the  electric  light.     Place  in  the  arc  a  few  crystals  of  sodium  nitrate. 


268 


LIGHT 


The  intense  heat  will  vaporize  the  sodium,  and  a  spectrum  will  be 
obtained  consisting  of  bright  colored  lines,  one  red,  one  yellow,  three 
green,  and  one  violet,  the  yellow  being  most  prominent. 

The  experiment  illustrates  discontinuous  or  bright  line 
spectra,  that  is,  spectra  consisting  of  one  or  more  bright 
lines  of  color  separated  by  dark  spaces.  Rarefied  gases 
and  vapors,  when  heated  to  incandescence,  give  discontinuous 
spectra. 

307.  Absorption  Spectra.  —  Project  on  the  screen  the  spectrum 
of  the  electric  light.     Between  the  lamp  and  the  slit  S  (Fig.  292) 

vaporize  metallic  so- 
dium in  an  iron 
spoon  so  placed  that 
the  white  light  passes 
through  the  heated 
sodium  vapor  before 
dispersion  by  the 
prism.  A  dark  line 
will  appear  on  the 
screen  in  the  yellow 
of  the  spectrum  at 
the  place  where  the 
bright  line  was  ob- 
tained in  the  preced- 
ing experiment. 

The  experiment  illustrates  an  absorption,  reversed  or  dark 
line  spectrum.  The  dark  line  is  produced  by  the  absorption 
of  the  yellow  light  by  sodium  vapor.  G-ases  and  vapors 
absorb  light  of  the  same  refrangibility  as  they  emit  at  a 
higher  temperature. 

308.  The  Fraunhofer  Lines.  —  Show  on  the  screen  a  carefully 
focused   spectrum   of   sunlight.     Several  of  the  colors  will  appear 
crossed  with  fine  dark  lines  (Fig.  293). 

Fraunhofer  was  the  first  to  notice  that  some  of  these 
lines  coincide  in  position  with  the  bright  lines  of  certain 


FIGURE  292.  —  ABSORPTION  SPECTRUM. 


THE  SPECTROSCOPE  269 

artificial  lights.  He  mapped  no  less  than  576  of  them, 
and  designated  the  more  important  ones  by  the  letters 
A,  B,  (7,  D,  U,  F,  6r,  H,  the  first  in  the  extreme  red  and 
the  last  in  the  vio- 
let. For  this  reason 
they  are  referred  to 

as   the    Fraunhofer 

,.  T  FIGURE  293.  —  FRAUNHOFER  LINES. 

lines.       In      recent 

years  the  number  of  these  lines  has  been  found  to  be 
practically  unlimited. 

In  the  last  experiment  it  was  shown  that  sodium  vapor 
absorbs  that  part  of  the  light  of  the  electric  arc  which  is 
of  the  same  refrangibility  as  the  light  emitted  by  the 
vapor  itself.  Similar  experiments  with  other  substances 
show  that  every  substance  has  its  own  absorption  spec- 
trum. These  facts  suggested  the  following  explanation 
of  the  Fraunhofer  lines  :  The  heated  nucleus  of  the  sun 
gives  off  light  of  all  degrees  of  refrangibility.  Its  spec- 
trum would  therefore  be  continuous,  were  it  not  sur- 
rounded by  an  atmosphere  of  metallic  vapors  and  of  gases, 
which  absorb  or  weaken  those  rays  of  which  the  spectra 
of  these  vapors  consist.  Hence,  the  parts  of  the  spec- 
trum which  would  have  been  illuminated  by  those  par- 
ticular rays  have  their  brightness  diminished,  since  the 
rays  from  the  nucleus  are  absorbed,  and  the  illumination 
is  due  to  the  less  intense  light  coming  from  the  vapors. 
These  absorption  lines  are  not  lines  of  no  light,  but  are 
lines  of  diminished  brightness,  appearing  dark  by  contrast 
with  the  other  parts  of  the  spectrum. 

309.  The  Spectroscope.  —  The  commonest  instrument  for 
viewing  spectra  is  the  spectroscope  (Fig.  294).  In  one 
of  its  simplest  forms  it  consists  of  a  prism  A,  a  telescope 
.B,  and  a  tube  called  the  collimator  C,  carrying  an  adjust- 


270  LIGHT 

able  slit  at  the  outer  end  J9,  and  a  converging  lens  at  the 
other  J$,  to  render  parallel  the  diverging  rays  coming  from 

A 
B       .         .nan  /^ftu^^L  D 


FIGURE  294.  —  SPECTROSCOPE. 


the  slit.  The  slit  must  therefore  be  placed  at  the  princi- 
pal focus  of  the  converging  lens.  To  mark  the  deviation 
of  the  spectral  lines,  there  is  provided  on  the  supporting 


FIGURE  295.  —  IRON  VAPOR  IN  THE  SUN. 

table  a  divided  circle  F,  which  is  read  by  the  aid  of 
verniers  and  reading  microscopes  attached  to  the  tele- 
scope arm. 

The  applications  of  the  spectroscope  are  many  and  various.     By 
an  examination  of  their  absorption  spectra,  normal  and  diseased,  blood 


VARIOUS     SPECTRA 


COLOR   OF  OPAQUE  BODIES  271 

are  easily  distinguished,  the  adulteration  of  substances  is  detected, 
and  the  chemistry  of  the  stars  is  approximately  determined.  Figure 
295  shows  the  agreement  of  a  number  of  the  spectral  lines  of  iron 
with  Fraunhofer  lines  in  the  solar  spectrum;  they  indicate  the  pres- 
ence of  iron  vapor  in  the  atmosphere  of  the  sun. 

VIII.   COLOR 

310.  The  Wave  Length  of   light   determines    its   color. 
Extreme  red  is  produced  by  the  longest  waves,  and  ex- 
treme violet  by  the  shortest.     The  following  are  the  wave 
lengths  for  the  principal  Fraunhofer  lines  in  air  at  20°  C. 
and  760  mm.  pressure  : 

A  Dark  Red  .  0.0007621  mm.  El  Light  Green  0.0005270  mm. 

B  Red   .     .     .  6884  mm.  E2 5269  mm. 

C  Orange  .    .  6563  mm.  F  Blue  .     .     .  4861  mm. 

Dl  Yellow   .     .  5896  mm.  G  Indigo    .     .  4293  mm. 

Z>2 5890  mm.  Hl  Violet     .     .  3968  mm. 

In  white  light  the  number  of  colors  is  infinite,  and  they 
pass  into  one  another  by  imperceptible  gradations  of  shade 
and  wave  length.  Color  stands  related  to  light  in  the 
same  way  that  pitch  does  to  sound.  In  most  artificial 
lights  certain  colors  are  either  feeble  or  wanting.  Hence, 
artificial  lights  are  not  generally  white,  but  each  one  is 
characterized  by  the  color  that  predominates  in  its 
spectrum. 

311.  Color  of  Opaque  Bodies.  —  Project  the  solar  spectrum  on  a 
white  screen.     Hold  pieces  of  colored  paper  or  cloth  successively  in 
different  parts  of  the  spectrum.     A  strip  of  red  flannel  appears  bril- 
liantly red  in  the  red  part  of  the  spectrum,  and  black  elsewhere ;   a 
blue  ribbon  is  blue  only  in  the  blue  part  of  the  spectrum,  and  a  piece 
of  black  paper  is  black  in  every  part  of  the  spectrum. 

The  experiment  shows  that  the  color  of  a  body  is  due  both 
to  the  light  that  it  receives  and  the  light  that  it  reflects  ; 


272  LIGHT 

that  a  body  is  red  because  it  reflects  chiefly,  if  not  wholly, 
the  red  rays  of  the  light  incident  upon  it,  the  others  being 
absorbed  wholly  or  partly  at  its  surface.  It  cannot  be  red 
if  there  is  no  red  light  incident  upon  it.  In  the  same  way 
a  body  is  white  if  it  reflects  all  the  rays  in  about  equal 
proportions,  provided  white  light  is  incident  upon  it.  So 
it  appears  that  bodies  have  no  color  of  their  own,  since 
they  exhibit  no  color  not  already  present  in  the  light 
which  illuminates  them. 

This  truth  is  illustrated  by  the  difficulty  experienced  in 
matching  colors  by  artificial  lights,  and  by  the  changes  in 
shades  some  fabrics  undergo  when  taken  from  sunlight  into 
gaslight.  Most  artificial  lights  are  deficient  in  blue  and 
violet  rays;  and  hence  all  complex  colors,  into  which  blue 
or  violet  enters,  as  purple  and  pink,  change  their  shade 
when  viewed  by  artificial  light. 

312.  Color  of  Transparent  Bodies.  —  Throw  the  spectrum  of 
the  sun  or  of  the  arc  light  on  the  screen.  Hold  across  the  slit  a  flat 
bottle  or  cell  filled  with  a  solution  of  amraoniated  oxide  of  copper.1 
The  spectrum  below  the  green  will  be  cut  off.  Substitute  a  solution 
of  picric  acid,  and  the  spectrum  above  the  green  will  be  cut  off.  Place 
both  solutions  across  the  slit  and  the  green  alone  remains.  It  is  the 
only  color  transmitted  by  both  solutions.  In  like  manner,  blue  glass 
cuts  off  the  less  refrangible  part  of  the  spectrum,  ruby  glass  cuts  off 
the  more  refrangible,  and  the  two  together  cut  off  the  whole. 

This  experiment  shows  that  the  color  of  a  transparent 
body  is  determined  by  the  colors  that  it  absorbs.  It  is 
colorless  like  glass  if  it  absorbs  all  colors  in  like  proportion, 
or  absorbs  none;  but  if  it  absorbs  some  colors  more  than 
others,  its  color  is  due  to  the  mixed  impression  produced 
by  the  various  colors  passing  through  it. 

1  It  is  prepared  by  adding  ammonia  to  a  solution  of  copper  sulphate, 
until  the  precipitate  at  first  formed  is  dissolved. 


THESE  PRIMARY  COLORS 


273 


313.  Mixing  Colored  Lights.  —  Out  of  colored  papers  cut  several 
disks,  about  15  cm.  in  diameter,  with  a  hole  at  the  center  for  mounting 
them  on  the  spindle  of  a  whirling  machine 
(Fig.  296),  or  for  slipping  them  over  the 
handle  of  a  heavy  spinning  top.  Slit  them 
along  a  radius  from  the  circumference  to 
the  center,  so  that  two  or  more  of  them 
can  be  placed  together,  exposing  any  pro- 
portional part  of  each  one  as  desired  (Fig. 
297).  Select  seven  disks,  whose  colors  most 
nearly  represent  those  of  the  solar  spec- 
trum ;  put  them  together  so  that  equal  por- 
tions of  the  colors  are  exposed.  Clamp  on 
the  spindle  of  the  whirling  machine  and 
rotate  them  rapidly.  When  viewed  in  a 
strong  light  the  color  is  an  impure  white 
or  gray. 


FIGURE  296.  —  MIXING 
COLORED  LIGHTS. 


This  method  of  mixing  colors  is 
based  on  the  physiological  fact  that 
a  sensation  lasts  longer  than  the 
stimulus  producing  it.  Before  the  sensation  caused  by  one 
stimulus  has  ceased,  the  disk  has  moved,  so  that  a  different 
impression  is  produced.  The  effect  is  equivalent  to 
superposing  the  several  colors  on  one 
another  at  the  same  time. 

314.  Three  Primary  Colors.  —  If  red, 
green,  and  blue,  or  violet  disks  are 
used,  as  in  §  313,  exposing  equal  por- 
tions, gray  or  impure  white  is  ob- 
tained when  they  are  rapidly  rotated.  If  any  two  colors 
standing  opposite  each  other  in  Fig.  298  are  used,  the  re- 
sult is  white;  and  if  any  two  alternate  ones  are  used,  the 
result  is  the  intermediate  one.  By  using  the  red,  the 
green,  and  the  violet  disks,  and  exposing  in  different  pro- 
portions, it  has  been  found  possible  to  produce  any  color 


FIGURE  297.  —  COLORED 
DISKS. 


274  LIGHT 

of  the  spectrum.  This  fact  suggested  to  Dr.  Young  the 
theory  that  there  are  only  three  primary  color  sensations, 
and  that  our  recognition  of  different  colors  is  due  to  the 

excitation  of  these  three  in  vary- 
ing degrees. 

The  color  top  is  a  standard 
toy  provided  with  colored  paper 
disks,  like  those  of  Fig.  296. 
When  red,  green,  and  blue  disks 
are  combined  so  as  to  show  sec- 
tors of  equal  size,  the  top,  when 
spinning  in  a  strong  light,  ap- 
pears  to  be  gray.  Gray  is  a 

30LORD.SK.          whjte      of      low      intengity          The 

colors  of  the  disks  are  those  of  pigments,  and  they  are  not 
pure  red,  green,  and  blue. 

315.  Three-  and  Four-color  Printing.  —  The  frontispiece 
of  this  book  illustrates  a  four-color  print  of  much  interest. 
Such  a  print  is  made  up  of  very  fine  lines  and  dots  of  the 
four  pigments,  red,  yellow,  blue,  and  black.  The  various 
colors  in  the  picture  are  mixtures  of  these  four  with  the 
white  of  the  paper. 

The  picture  is  made  by  printing  the  four  colors  one  on 
top  of  the  other  from  four  copper  plates,  each  of  which 
represents  only  that  part  of  the  picture  where  a  certain 
color  must  be  used  to  give  the  proper  final  effect.  These 
plates  are  made  from  four  negatives.  The  process  of  pre- 
paring these  negatives  is  as  follows  : 

Each  negative  is  made  by  taking  a  picture  of  the  origi- 
nal colored  drawing  through  a  colored  "filter,"  which  cuts 
out  all  the  colors  except  the  one  desired.  A  blue  filter  is 
used  to  prepare  the  plate  that  prints  with  yellow  ink,  a 
green  filter  to  prepare  the  red  printing  plate,  a  red  filter 


MIXING  PIGMENTS  275 

for  the  blue  printing  plate,  and  a  chrome  yellow  filter  fot 
the  black  printing  plate. 

A  cross-lined  glass  screen,  dividing  the  image  into  small 
dots,  is  placed  in  front  of  the  negatives  in  the  camera. 
Glue  enamel  prints  are  then  made  on  copper,  and  the  plates 
are  etched,  leaving  the  desired  pri  ting  surface  in  relief. 

In  the  frontispiece  the  yellow  is  printed  first,  the  red 
over  the  }^ellow  second,  the  blue  third  over  the  yellow  and 
red,  and  the  black  last  over  the  yellow,  red,  and  blue. 

When  no  black  is  used  the  process  is  known  as  the 
three-color  process. 

316.  Complei  entary  Colors. — Any  two  colors  whose  mix- 
ture produces  on  the  eye  the  impression  of  white  light  are 
called   complementary.     Thus,  red   and  bluish  green   are 
complementary ;    also    orange    and   light    blue.       When 
complementary  colors  are  viewed  next  to  each  other,  the 
effect  is  a  mutual  heightening  of  color  impressions. 

Complementary  colors  may  be  seen  by  what  is  known  as  retinal 
fatigue.  Cut  some  design  out  of  paper,  and  paste  it  on  red  glass. 
Project  it  on  a  screen  in  a  dark  room.  Look  steadily  at  the  screep 
for  several  seconds,  and  then  turn  up  the  lights.  The  design  will 
appear  on  a  pale  green  ground. 

This  experiment  shows  that  the  portion  of  the  retina 
on  which  the  red  light  falls  becomes  tired  of  red,  and 
refuses  to  convey  as  vivid  a  sensation  of  red  as  of  the 
other  colors,  when  less  intense  white  light  is  thrown  on 
it.  But  it  retains  its  sensitiveness  in  full  for  the  rest  of 
white  light,  and  therefore  conveys  to  the  brain  the  im- 
pression of  white  light  with  the  red  cut  out ;  that  is,  of 
the  complementary  color,  green. 

317.  Mixing  Pigments.  —  Draw  a  broad  line  on  the  blackboard 
with  a  yellow  crayon.     Over  this  draw  a  similar  band  with  a  blue 
crayon.     The  result  will  be  a  band  distinctly  green. 


276  LIGHT 

The  yellow  crayon  reflects  green  light  as  well  as  yel- 
low, and  absorbs  all  the  other  colors.  The  blue  crayon 
reflects  green  light  along  with  the  blue,  absorbing  all 
the  others.  Hence,  in  superposing  the  two  chalk  marks, 
the  mixture  absorbs  all  but  the  green.  The  mark  on  the 
board  is  green,  because  that  is  the  only  color  that  sur- 
vives the  double  -absorption.  In  mixing  pigments,  the 
resulting  color  is  the  residue  of  a  process  of  successive 
absorptions.  If  the  spectral  colors,  blue  and  yellow,  are 
mixed,  the  product  is  white  instead  of  green.  So  we  see 
that  a  mixture  of  colored  lights  is  a  very  different  thing 
from  a  mixture  of  pigments. 

IX.   INTERFERENCE  AND  DIFFRACTION 

318.  Newton's  Rings.  —  Press  together  at  their  center  two  small 
pieces  of  heavy  plate  glass,  using  a  small  iron  clamp  for  the  purpose. 
Then  look  obliquely  at  the  glass ;  curved  bands  of  color  may  be  seen 
surrounding  the  point  of  greatest  pressure. 

This  experiment  is  like  one  performed  by  Newton 
while  attempting  to  determine  the  relation  between  the 
colors  in  the  soap  bubble  and  the  thickness  of  the  film. 
He  used  a  plano-convex  lens  of  long  focus  resting  on  a 

plate  of  plane  glass.  Figure  299 
'B  shows  a  section  of  the  apparatus. 

Between  the  lens  and  the  plate 
FIGURE  299.  — NEWTON s  there  is  a  wedge-shaped  film  of 

air,  very  thin,  and  quite  similar  to 

that  formed  between  the  glass  plates  in  the  above  experi- 
ment. If  the  glasses  are  viewed  by  reflected  light,  there 
is  a  dark  spot  at  the  point  of  contact,  surrounded  by  sev- 
eral colored  rings  (Fig.  300)  ;  but  if  viewed  by  trans- 
mitted light,  the  colors  are  complementary  to  those  seen 
by  reflection  (§  316). 


NEWTON'S  KINGS 


277 


FIGURE  300.  —  COLORED 
RINGS. 


The  explanation  is  to  be  found  in  the  interference  of 
two  sets  of  waves,  one  reflected  internally  from  the 
curved  surface  ACS,  and  the  other  from  the  surface 
D  CE,  on  which  it  presses.  If  light 
of  one  color  is  incident  on  AB,  a 
portion  will  be  reflected  ivomACB, 
and  another  portion  from  DOE. 
Since  the  light  reflected  from  DOE 
has  traveled  farther  by  twice  the 
thickness  of  the  air  film  than  that 
from  AGB,  and  the  film  gradually 
increases  in  thickness  from  C  out- 
ward, it  follows  that  at  some  places 
the  two  reflected  portions  will  meet 
in  like  phase,  and  at  others  in  opposite  phase,  causing  a 
strengthening  of  the  light  at  the  former,  and  extinction 
of  it  at  the  latter. 

If  red  light  be  used,  the  appearance  will  be  that  of  a 
series  of  concentric  circular  red  bands  separated  by  dark 
ones,  each  shading  off  into  the  other.  If  violet  light  be 
employed,  the  colored  bands  will  be  closer  together  on 
account  of  the  shorter  wave  length.  Other  colors  will 
give  bands  intermediate  in  diameter  between  the  red 
and  violet.  From  this  it  follows  that  if  the  glasses  be 
illuminated  by  white  light,  at  every  point  some  one  color 
will  be  destroyed.  The  other  colors  will  be  either  weak- 
ened or  strengthened,  depending  on  the  thickness  of  the 
air  film  at  the  point  under  consideration,  the  color  at 
each  point  being  the  result  of  mixing  a  large  number  of 
colors  in  unequal  proportions.  Hence,  the  point  C  will 
be  surrounded  by  a  series  of  colored  bands.1 

1  The  light  from  ACB  differs  in  phase  half  a  wave  length  from  that 
reflected  from  DE,  because  the  former  is  reflected  in  an  optically  dense 


278  LIGHT 

The  colors  of  the  soap  bubble,  of  oil  on  water,  of  heated 
metals  which  easily  oxidize,  of  a  thin  film  of  varnish,  and 
of  the  surface  of  very  old  glass,  are  all  caused  by  the  in- 
terference of  light  reflected  from  the  two  surfaces  of  a 
very  thin  film. 

319.  Diffraction.  —  Place  two  superposed  pieces  of  perforated 
cardboard  in  front  of  the  condenser  of  the  projection  lantern.  The 
projected  images  of  the  very  small  holes,  as  one  piece  is  moved  across 
the  other,  are  fringed  with  the  spectral  colors. 

With  a  fine  diamond  point  rule  a  number  of  equidistant  parallel 
lines  very  close  together  on  glass.  They  compose  a  transparent  dif- 
fraction grating.  Substitute  this  for  the  prism  in  projecting  the  spec- 
trum of  sunlight  or  of  the  arc  light  on  the  screen  (§  300).  There 
will  be  seen  on  the  screen  a  central  image  of  the  slit,  and  on  either 
side  of  it  a  series  of  spectra.  Cover  half  of  the  length  of  the  slit  with 
red  glass  and  the  other  half  with  blue.  There  will  now  be  a  series 
of  red  images  and  also  a  series  of  blue  ones,  the  red  ones  being  far- 
ther apart  than  the  blue.  Lines  ruled  close  together  on  smoked 
glass  may  be  used  instead  of  a  "grating." 

These  experiments  illustrate  a  phenomenon  known  as 
diffraction.  The  colored  bands  are  caused  by  the  inter- 
ference of  the  waves  of  light  which  are  propagated  in  all 
directions  from  the  fine  openings.  The  effects  are  visible 
because  the  transparent  spaces  are  so  small  that  the  inten- 
sity of  the  direct  light  from  the  source  is  largely  re- 
duced. Diffraction  gratings  are  also  made  to  operate  by 
reflecting  light.  Striated  surfaces,  like  mother-of-pearl, 
changeable  silk,  and  the  plumage  of  many  birds,  owe 
their  beautiful  changing  colors  to  interference  of  light  by 
diffraction. 


medium  next  to  a  rare  one,  and  the  latter  in  an  optically  rare  medium 
next  to  a  dense  one.  This  phase  difference  is  additional  to  the  one  above 
described. 


QUESTIONS  279 

Questions 

1.  How  many  degrees  is  it  from  the  sun  to  the  highest  point  of  the 
primary  rainbow  ? 

2.  Why  is  the  red  on  the  outside  of  the  primary  bow  and  on  the 
inside  of  the  secondary  bow  ? 

3.  If  there  are  but  three  primary  sensations,  red,  green,  and  violet, 
what  effect  would  it  have  on  a  person's  vision  if  the  nerves  for  red 
sensations  were  inoperative  ? 

4.  Why  is  the  secondary  rainbow  less  bright  than  the  primary 
bow? 

5.  Are  the  two  images  of  an  object  as  formed  on  the  retina  of  the 
two  eyes  identical  ?     Explain. 

6.  Account  for  the  crossed  bands  of  light  seen  by  looking  through 
the  wire  screening  of  the  window  at  the  full  moon. 

7.  Account  for  the  change  in  color  of  aniline  purple  when  viewed 
by  the  light  of  a  common  kerosene  lamp. 

8.  Under  what  conditions  could  a  rainbow  be  seen  at  midday? 

9.  Account  for  the  colors  on  water  when  gasoline  is  poured  on  it. 
10.    Why  does  each  person  in  using  a  microscope  have  to  focus  for 

his  own  eyes  ? 


CHAPTER   IX 

HEAT 
I.   HEAT  AND  TEMPERATURE 

320.  Nature  of  Heat.  —  For  a  long  time  it  was  believed 
that  heat  was  a  subtle  and  weightless  fluid  that  entered 
bodies  and  possibly  combined  with  them.     This  fluid  was 
called  calorie.     About  the  beginning  of  the  last  century 
some  experiments  of  Count  Rumford  in  boring  brass  can- 
non, and  those  of  Sir  Humphry  Davy  in  melting  two  pieces 
of  ice  at  freezing  temperature  by  the  friction  of  one  piece 
on  the  other  demonstrated  that  the  caloric  theory  of  heat 
was  no  longer  tenable ;  and  finally  about  the  middle  of 
the  century,  when  Joule  proved  that  a  definite  amount  of 
mechanical  work  is   equivalent  to  a  definite  amount  of 
heat,  it  became  evident  that  heat  is  a  form  of  molecular 
energy. 

The  modern  kinetic  theory,  briefly  stated,  is  as  follows : 
The  molecules  of  a  body  have  a  certain  amount  of  inde- 
pendent motion,  generally  very  irregular.  Any  increase 
in  the  energy  of  this  motion  shows  itself  in  additional 
warmth,  and  any  decrease  by  the  cooling  of  the  body. 
The  heating  or  the  cooling  of  a  body,  by  whatever 
process,  is  but  the  transference  or  the  transformation  of 
energy. 

321.  Temperature.  —  If  We  place  a  mass  of  hot  iron  in 
contact  with  a  mass  of  cold  iron,  the  latter  becomes  warmer 
and  the  former  cooler,  the  heat  flowing  from  the  hot  body 

280 


MEASURING   TEMPERATURE  281 

to  the  cold  one.  The  two  bodies  are  said  to  differ  in  tem- 
perature or4' heat  level,"  and  when  they  are  brought  in 
contact  there  is  a  flow  of  heat  from  the  one  of  higher  tem- 
perature to  the  one  of  lower  until  thermal  (heat)  equilib- 
rium is  established. 

Temperature  is  the  thermal  condition  of  a  body  which 
determines  the  transfer  of  heat  between  it  and  any  body 
in  contact  with  it.  This  transfer  is  always  from  the  body 
of  higher  temperature  to  the  one  of  lower.  Temperature 
is  a  measure  of  the  degree  of  hotness ;  it  depends  solely  on 
the  kinetic  energy  of  the  molecules  of  the  body. 

Temperature  must  be  distinguished  from  quantity  of 
heat.  The  water  in  a  pint  cup  may  be  at  a  much  higher 
temperature  than  the  water  in  a  lake,  yet  the  latter  con- 
tains a  vastly  greater  quantity  of  heat,  owing  to  the 
greater  quantity  of  water. 

322.  Measuring  Temperature.  —  Fill  three  basins  with  mod- 
erately hot  water,  cold  water,  and  tepid  water  respectively.  Hold  one 
hand  in  the  first,  and  the  other  in  the  second  for  a  short  time ;  then 
transfer  both  quickly  to  the  tepid  water.  It  will  feel  cold  to  the 
hand  that  has  been  in  hot  water  and  warm  to  the  other.  Hold  the 
hand  successively  against  a  number  of  the  various  objects  in  the  room, 
at  about  the  same  height  from  the  floor.  Metal,  slate,  or  stone  ob- 
jects will  feel  colder  than  those  of  wood,  even  when  side  by  side  and 
of  the  same  temperature. 

These  experiments  show  that  the  sense  of  touch  does 
not  give  accurate  information  regarding  the  relative  tem- 
perature of  bodies,  and  some  other  method  must  be  re- 
sorted to  for  reliable  measurement.  The  one  most  ex- 
tensively used  is  based  on  the  regular  increase  in  the  vol- 
ume of  a  body  attending  a  rise  in  its  temperature.  This 
method  is  illustrated  by  the  common  mercurial  ther- 
mometer. 


282 


HEAT 


70°! 


II.   THE  THERMOMETER 

323.   The  Thermometer.  —  The    common   mercurial   ther- 
mometer consists  of  a  capillary  glass  tube  of  uniform  bore, 
on  one  end  of  which  is  blown  a  bulb,  either 

ft        V 

spherical  or  cylindrical  (Fig.  301).  Part  of 
the  air  is  expelled  by  heating,  and  while  in 
this  condition  the  open  end  of  the  tube  is 
dipped  into  a  vessel  of  pure  mercury.  As 
the  tube  cools,  mercury  is  forced  into  the 
tube  by  atmospheric  pressure.  Enough  mer- 
cury is  introduced  to  fill  the  bulb  and  part 
of  the  tube  at  the  lowest  temperature  which 
the  thermometer  is  designed  to  measure. 
Heat  is  now  applied  to  the  bulb  until  the  ex- 
panded mercury  fills  the  tube ;  the  end  is 
then  closed  in  the  blowpipe  flame.  The 
mercury  contracts  as  it  cools,  leaving  the 
larger  portion  of  the  capillary  empty. 

324.  The  Necessity  of  Fixed  Points.  —  No 
two  thermometers  are  likely  to  have  bulbs 
and  stems  of  the  same  capacity.  Conse- 
quently, the  same  increase  of  temperature 
will  not  produce  equal  changes  in  the  length  of  the  thread 
of  mercury.  If,  then,  the  same  scale  were  attached  to  all 
thermometers,  their  indications  would  differ  so  widely 
that  the  results  would  be  worthless.  Hence,  if  ther- 
mometers are  to  be  compared,  corresponding  divisions  on 
the  scale  of  different  instruments  must  indicate  the  same 
temperature.  This  may  be  done  by  graduating  every 
thermometer  by  comparison  with  a  standard,  an  expensive 
proceeding  and  for  many  purposes  unnecessary,  since  mer- 
cury has  a  nearly  uniform  rate  of  expansion.  If  two 


FIGURE  301. 
—  C.  AND  F. 
THERMOME- 
TERS.  • 


MARKING   THE  FIXED  POINTS 


283 


points  are  marked  on  the  stem,  the  others  can  be  obtained 
by  dividing  the  space  between  them  into  the  proper  num- 
ber of  equal  parts.     Investigations  have  made  it 
certain  that  under  a  constant  pressure  the  tem- 
perature of  melting  ice  and  that  of  steam  are  in- 
variable.    Hence,  the  temperature  of  melting  ice 
and  that  of  steam  under  a  pressure  of  76  cm.  of 
mercury  (one  atmosphere)  have  been  chosen  as 
the  fixed  points  on  a  thermometer. 

325.  Marking  the  Fixed  Points.  —  The  ther- 
mometer is  packed  in  finely  broken  ice,  as  far  up 
the  stem  as  the  mercury  extends.  The  contain- 
ing vessel  (Fig.  302)  has  an  opening  at  the  bot- 
tom to  let  the  water  run  out.  After  standing  in 
the  ice  for  several  minutes  the 
top  of  the  thread  of  mercury  is 
marked  on  the  stem.  This  is 
called  the  freezing  point. 

The  boiling  point  is  marked  by  observ- 
ing the  top  of  the  mercurial  column  when 
the  bulb  and  stem  are  enveloped  in  steam 
(Fig.  303)  under  an  atmospheric  pressure 
of  76  cm.  (29.92  in.).  If  the  pressure  at 
the  time  is  not  76  cm.,  then  a  correction 
must  be  applied,  the  amount  being  de- 
termined by  the  approximate  rule  that 
the  temperature  of  steam  rises  0.1°  C. 
for  every  increase  of  2.71  mm.  in  the 
barometric  reading,  near  100°  C. 

326.  Thermometer  Scales.  —  The  dis- 
tance between  the  fixed  points  is  divided 
into  equal  parts  called  degrees.  The  number  of  such  parts 
is  wholly  arbitrary,  and  several  different  scales  have  been 


FIGURE 
302  .  — 
FREEZING 
POINT. 


FIGURE  303.  — 
MARKING  THE  BOIL- 
ING POINT. 


284  HEAT 

introduced.  The  number  of  thermometer  scales  in  use  in 
the  eighteenth  century  was  at  least  nineteen.  Fortunately 
all  but  three  of  them  have  passed  into  ancient  history. 

The  Fahrenheit  scale,  which  is  in  general  use  in  English- 
speaking  countries,  appears  to  have  made  its  first  appear- 
ance about  1714, 'but  the  earliest  published  description  of 
it  was  in  1724.  At  that  time  this  scale  began  at  0°  and 
ended  at  96°.  Fahrenheit  describes  his  scale  as  deter- 
mined by  three  points :  the  lowest  was  the  0°  and  was 
found  by  a  mixture  of  ice,  water,  and  sea  salt ;  the  next 
was  the  32°  point  and  was  found  by  dipping  the  ther- 
mometer into  a  mixture  of  ice  and  water  without  salt ; 
the  third  was  marked  96°,  the  point  to  which  alcohol 
expanded  "if  the  thermometer  be  held  in  the  mouth  or 
armpit  of  a  healthy  person."  When  this  scale  was  ex- 
tended, the  boiling  point  was  found  to  be  212°.  The 
space  between  the  freezing  and  the  boiling  point  is  there- 
fore 180°. 

The  Centigrade  scale  was  introduced  by  Celsius,  pro- 
fessor of  astronomy  in  the  University  of  Upsala,  about 
1742.  It  differs  from  the  Fahrenheit  in  making  the  freez- 
ing point  0°  and  the  boiling  point  100°,  the  space  between 
being  divided  into  100  equal  parts  or  degrees.  The  sim- 
plicity of  Celsius's  division  of  the  scale  has  led  to  its 
general  adoption  in  all  countries  for  scientific  purposes, 
and  in  many  for  domestic  and  industrial  use. 

The  scale  in  both  thermometers  is  extended  beyond  the 
fixed  points  as  far  as  desired.  The  divisions  below  0° 
are  read  as  minus  and  are  marked  with  the  negative  sign. 
The  initial  letters  F.  and  C.  denote  the  Fahrenheit  and 
Centigrade  scales  respectively. 

327.  The  Two  Scales  Compared.  —  In  Fig.  304  AB  is 
a  thermometer  with  two  scales  attached,  P  is  the  head 


THE  CLINICAL   THERMOMETER  285 

of  the  mercury  column,  and  F  and  O  are  the  readings 
on  the  scales  respectively.  On  the  Fahrenheit  scale, 
AB  =  ISQ  and  AP  ^^^  * 
=  ^—32,  since  the  <^^* 


zero  is  32  spaces  be-    FahreDheit   3,2 


Centigrade 


O  100 


low  A'9    on  the  Centi-  FIGURE  304.-- SCALES  COMPARED. 

grade,  AB  =  100  and 

AP  =  O.     Then  the  ratio  of  AP  to  AB  is  £JZ£f  =  _i_ . 

By  substituting  the  reading  on  either  scale  in  this  equa- 
tion the  equivalent  on  the  other  scale  is  easily  obtained. 
For  example,  if  it  is  required  to  express  68°  F.  on  the 

^»O   OO  i~1 

Centigrade    scale,    then    —          =  — — ;    whence 
C  —  20° 

328.  Limitations  of  the  Mercurial  Thermometer. — 
As  mercury  freezes  at  —  38.8°  C.,  it   cannot  be 
used  as  the  therm ometric  substance   below   this 
temperature.     For  temperatures  below  —  38°  C. 
alcohol  is  substituted  for  mercury.     Under  a  pres- 
sure  of   one  atmosphere  mercury   boils  at  about 
350°  C.     For  temperatures  approaching  this  value 
and  up  to  about  550°  C.  the  thermometer  stem  is 
filled  with  pure  nitrogen   under    pressure.     The 
pressure  of  the  gas  keeps  the  mercury  from  boiling 
(§  356). 

329.  The   Clinical   Thermometer.  -^  The    clinical 
thermometer  is   a   sensitive  instrument  of   short 
range  for  indicating  the  temperature  of  the  human 
body.     It  is  usually  graduated  from  95°  to  110° 

FIGURE  ^.,  or  from  35°  to  45°  C.  There  is  a  constriction 
305.  —  in  the  tube  just  above  the  bulb  (Fig.  305),  which 
TL^C^  causes  the  thread  of  mercury  to  break  at  that  point 
MOMETER.  when  the  temperature  begins  to  fall,  leaving  the 


286  HEAT 

top  of  the  separated  thread  to  mark  the  highest  tempera- 
ture registered.  A  sudden  jerk  or  tapping  of  the  ther- 
mometer forces  the  mercury  down  past  the  constriction 
and  sets  it  for  a  new  reading.  The  normal  temperature 
of  the  human  body  is  98.6°  F.  or  37°  C. 

Questions  and  Problems 

1.  Why  do  the  degree  spaces  differ  in  length  on  different  ther- 
mometers of  the  same  scale  ? 

2.  What  advantages  does  a  thermometer  with  a  cylindrical  bulb 
have  over  one  with  a  spherical  bulb  ? 

3.  Why  is  mercury  preferable  to  other  liquids  for  use  in  ther- 
mometers ? 

4.  Why  is  it  necessary  to  have  fixed  points  in  thermometers? 

5.  The  bulb  of  a  thermometer  generally  contracts  a  little  after 
the  thefmometer  is  completed.     What  is  the  result  on  the  readings? 

6.  Why  is  nitrogen  used  in  preference  to  oxygen  in  thermometers 
for  high  temperatures  ? 

7.  Why  should  the  thermometer  tube  be  of  uniform  bore? 

8.  Express   in   Fahrenheit  degrees   the  following  4°  C.,  30°  C., 
-  38°  C. 

9.  Express  in  Centigrade  degrees  the  following  39°  F.,  -  40°  F., 
68°  F. 

10.  The  fixed  points  on  a  Centigrade  thermometer  were  found  to 
be  incorrect;  the  freezing  point  read  2°  and   the  boiling  point  99°. 
When  this  thermometer  was  immersed  in  a  liquid  the  reading  was 
50°.     What  was  the  correct  temperature  of  the  liquid  ? 

(NOTE.  —  Compare  this  incorrect  thermometer  with  a  correct  one 
just  as  a  Fahrenheit  thermometer  is  compared  with  a  Centigrade  in 
§  327.) 

11.  A  thermometer  read  40°  C.  in  a  water  bath.     When  tested  it 
was  found  to  read  0°  at  the  freezing  point,  but  95°  instead  of  100°  at 
the  boiling  point.     What  was  the  correct  temperature  of  the  bath  ? 

12.  If  a  Fahrenheit  thermometer  read  210°  in  steam  and  31°  in 
melting  ice,  what  would  it  read  as  the  equivalent  of  70°  F.  ? 


EXPANSION  OF  SOLIDS 


287 


13.  A  correct  Fahrenheit  thermometer  read  70°  as  the  temperature 
of  a  room.     An  incorrect   Centigrade  thermometer  read  20°  in  the 
same  room.     What  was  the  error  of  the  latter? 

14.  A  certain  Centigrade  thermometer  reads  2°  in  melting  ice  and 
100°   in   steam  under  normal   atmospheric   pressure.     What  is  the 
correct  value  for  a  reading  of  25°  on  this  thermometer  ? 


III.   EXPANSION 

330.  Expansion  of  Solids.  —  Insert  a  long  knitting  needle  A 
in  a  block  of  wood  so  as  to  stand  vertically  (Fig.  306).  A  second 
needle  D  is  supported  paral- 
lel to  the  first  by  means  of  a 
piece  of  cork  or  wood  C. 
The  lower  end  of  D  just 
touches  the  mercury  in  the 
cup  H.  An  electric  circuit 
is  made  through  the  mer- 
cury, the  needle,  an  electric 
battery,  and  the  bell  B,  as 
shown.  Now  apply  a  Bun- 
sen  flame  to  A  ;  D  will  be 
lifted  out  of  the  mercury  and 
the  bell  will  stop  ringing. 
Then  heat  D  or  cool  A,  and 
th  e  contact  of  D  with  the  mer- 
cury will  be  renewed  as  shown 
by  the  ringing  of  the  bell. 


FIGURE  306.  —  SHOWING  EXPANSION. 


This  experiment  shows  that  solids  expand  in  length 
when  heated  and  contract  when  cooled.  To  this  rule  of 
expansion  there  are  a  few  exceptions,  notably  iodide  of  sil- 
ver and  stretched  india-rubber. 

Rivet  together  at  short  intervals  a  strip  of  sheet  copper  and  one  of 
sheet  iron  D  (Fig.  307).  Support  this  compound  bar  so  as  to  play 
between  two  points  A  and  C,  which  are  connected  through  the  battery 
P  and  the  bell  B.  Apply  a  Bunsen  flame  to  the  bar.  It  will  warp, 


288 


HEAT 


throwing  the  top  over  against  either  A  or  C,  and  will  cause  the  bell 
to  ring. 


FIGURE  307.  —  UNEQUAL  EXPANSION. 

The   experiment   shows  that   the   two   metals   expand 
unequally  and  cause  the  bar  to  warp. 

Figure  308  illustrates  a  piece  of  ap- 
paratus known  as  Gravesande's  ring. 
It  consists  of  a  metallic  ball  that  at 
ordinary  temperatures  will  just  pass 
through  the  ring.  Heat  the  ball  in 
boiling  water.  It  will  now  rest  on  the 
ring  and  will  not  fall  through  until  it 
has  cooled. 


FIGURE  308. —  EXPANSION  OF 
BALL. 


We  conclude  that  the  ex- 
pansion of  a  solid  takes  place 
in  every  direction. 

331.  Expansion  of  Liquids.  —  Select  two 
four-inch  test  tubes,  fit  to  each  a  perforated 
stopper,  through  which  passes  a  small  glass  tube 
about  six  inches  long.  The  capacity  of  the  two 
test  tubes  after  stoppers  are  inserted  should  be 
equal.  Fill  one  tube  with  mercury  and  the  other 
with  glycerine  colored  with  an  aniline  dye.  Set 
the  test  tubes  in  a  beaker  of  water  over  a  Bunsen 
flame  (Fig.  309)  and  note  the  change  in  the 
height  of  the  liquids  in  the  tubes. 

Two  facts  are  illustrated:  first,  liquids      _         Qno     _. 

.    '  FIGURE  OUV.  —  E.X- 

are  affected  by  heat  in  the  same  way  as    PANSION  OF  LIQUIDS. 


COEFFICIENT  OF  LINEAR  EXPANSION  289 

solids  ;  second,  the  expansion  of  the  liquids  is  greater  than 
that  of  the  glass  or  there  would  be  no  apparent  increase  in 
their  volume. 

Some  liquids  do  not  expand  when  heated  at  certain 
points  on  the  thermometric  scale.  Water,  for  example, 
on  heating  from  0°  C.  to  4°  C.  contracts,  but  above  4°  C. 
it  expands. 

332.  Expansion  of  Gases.  —  Fit  a  bent  delivery  tube  to  a  small 
Florence  flask  (Fig.  310).     Fill  the  flask  with  air  and  place  the  up- 
turned end  of  a  delivery  tube  under  an  inverted  graduated  glass 
cylinder  filled  with   water.     Heat 

the  flask  by  immersing  it  in  a 
vessel  of  moderately  hot  water. 
The  air  will  expand  and  escape 
through  the  delivery  tube  into 
the  cylinder;  note  the  amount. 
Now  refill  the  flask  with  some 
other  gas,  as  coal  gas,  and  re- 
peat the  experiment.  The  amount 
of  gas  collected  will  be  nearly  the 
same.  FIGURE  310.  —  EXPANSION  OF  GASES. 

Investigation  has  shown  that  all  gases  which  are  hard  to 
liquefy  expand  very  nearly  alike  at  atmospheric  pressure, 
approaching  equality  as  the  pressure  is  diminished.  Gases 
that  are  easily  liquefied,  as  carbon  dioxide,  show  the  largest 
variation  in  the  expansion. 

333.  Coefficient  of  Linear  Expansion.  —  Nearly  all  solids 
expand   with   increase   of   temperature,  but  they  do  not 
expand  equally.     Assume  three  rods  of  the  same  length,  — 
zinc,  brass,  and  steel.     With  the  same  rise  of  temperature, 
the  zinc  rod  will  increase  in  length  50  per  cent  more  than 
the  brass,  and  the  brass  nearly  50  per  cent  more  than  the 
steel.     A  brass  bar  will  expand   in   length   20   times  as 
much  as  a  bar  of  "  invar  "  (nickel  steel)  if  the  bars  are 


290  HEAT 

of   the  same   length   and   undergo   the   same   change   of 
temperature. 

The  coefficient  of  linear  expansion,  or  expansion  in  length, 
expresses  this  property  of  expansion  in  a  numerical  way. 
It  is  the  increase  in  a  unit  length  of  a  substance  per  degree 
increase  in  temperature.  This  is  equivalent  to  the  ex- 
pression : 

Coefficient  of  linear  expansion 

increase  in  length 


original  length  x  temp,  change 

If  Zj  and  £2  denote  the  lengths  of  a  metallic  rod  at  tem- 
peratures £j  and  £2  respectively,  then  2  ~  1  =  2  ~  1  is  the 

^2  ~~  *i          * 
whole  expansion  for  1° ;  t  is  the  difference  of  temperature. 

If  a  denotes  the  coefficient  of  expansion,  then  a  =  -2 1 ; 

whence  12  =  ^(1  +  at).  V 

Since  this  coefficient  is  a  ratio,  it  makes  no  difference 
what  unit  of  length  is  used.  Coefficients  of  expansion  are 
usually  given  in  terms  of  the  Centigrade  degree.  For 
the  Fahrenheit  degree  the  coefficient  is,  of  course,  J  as 
great  as  for  the  Centigrade. 

SOME  COEFFICIENTS  OF  LINEAR  EXPANSION 

Invar 0.0000009  Copper 0.0000172 

Glass 0.0000086  Brass 0.0000188 

Platinum      .     .     .     .  0.0000088  Silver 0.0000191 

Cast  Iron      ....  0.0000113  Tin 0.0000217 

Steel 0.0000132  Zinc 0.0000294 

334.  Illustrations  of  Linear  Expansion.  —  Many  familiar  facts 
are  accounted  for  by  expansion  or  contraction  attending  changes  of 
temperature.  If  hot  water  is  poured  into  a  thick  glass  tumbler,  the 
glass  will  probably  crack  by  reason  of  the  stress  produced  by  the 


BRIDGE  OVER  THE  FIRTH  OF  FORTH. 

Allowance  for  the  expansion  and  contraction  of  the  steel  must  be  made 
in  the  construction. 


COMPENSATED  CLOCKS  AND    WATCHES 


291 


sudden  expansion  of  its  inner  surface.  On  the  other  hand,  crucibles 
and  other  laboratory  utensils  are  now  made  of  clear  fused  quartz  ;  fused 
quartz  has  so  small  a  coefficient  of  expansion  that  a  red-hot  crucible 
may  be  plunged  into  water  without  cracking.  The  coefficients  of 
glass  and  platinum  are  so  nearly  equal  that  platinum  wires  may  be 
sealed  into  glass  without  cracking  the  latter  when  it  cools. 

Crystalline  rocks,  on  account  of  unequal  expansion  in  different 
directions,  are  slowly  disintegrated  by  changes  of  temperature  ;  and 
for  the  same  reason  quartz  crystals,  when  strongly  heated,  fly  in 
pieces.  The  outcropping  granite  hills  of  the  celebrated  South  African 
Matopos  have  been  broken  into  huge  boulders  and  irregular  masses 
by  the  large  expansion  in  the  fervid  heat  of  midday  and  the  subse- 
quent rapid  contraction  during  the  low  temperature  of  the  succeeding 
night. 

In  long  steel  bridges  built  in  cold  climates  considerable  expansion 
occurs  in  summer,  and  a  certain  freedom  of  motion  of  the  parts  must 
be  provided  for.  Long  suspension  bridges  are  several 
inches  higher  at  the  middle  in  midwinter  than  in  the  heat 
of  summer.  Long  steam  pipes  are  fitted  with  expansion 
joints  to  permit  one  part  to  slide  into  the  other  ;  bends  or 
elbows  in  the  pipe  are  also  used,  so  that  the  pipe  may  ac- 
commodate itself  to  the  expansion. 

335.  Compensated  Clocks  and  Watches.  —  If  the 
length  of  a  pendulum  changes  with  temperature,  the  period 
of  vibration  will  also  change  and  the  clock  will  not  have  a 
constant  rate.  The  balance  wheel  of  a  watch  serves  a 
similar  purpose  of  regulating  the  period  of  vibration  and 
is  similarly  affected  by  changes  in  temperature.  To  com- 
pensate for  these  changes  so  as  to  keep  the  period  of  vi- 
bration constant,  the  principle  of  unequal  expansion  is  em- 
ployed. 

The  bob  of  a  compensated  mercurial  pendulum  consists 
of  one  or  more  glass  jars,  nearly  filled  with  mercury,  and 
attached  to  the  lower  end  of  a  steel  rod  (Fig.  311).  A 
of  temperature  lengthens  the  rod  and  lowers  the 


rse 


FIGURE 
311.— 

M  ERCU- 

RIAL  PEN- 
DULUM. 


center  of  oscillation  ;   but  the  mercury  expands  upward 

and  compensates  by  raising  the  center  of  oscillation.     By 

a  proper  adjustment  of  the  quantity  of  mercury  in  the  tubes,  its 

expansion  may  be  made  to  compensate  for  that  of  the  rod. 


292       v  HEAT 

The  rate  of  a  watch  depends  largely  on  the  balance  wheel.     Unless 
this  is  compensated,  it  expands  when  the  temperature  rises  and  the 
watch  loses  time,  the   larger  wheel  oscillating 
more  slowly  under  the  force  supplied  by  the 
elasticity  of  the  hairspring.     Compensation  is 
secured  by  making  the  rim  of  the  wheel  in  two 
sections,  each  being  made  of  two  materials  and 
supported  by  one  end  on  a  separate  arm  (Fig. 
312).     The  more  expansible  metal  is  on  the  out- 
side.    When  the  temperature,  rises  and  the  radial 
FIGURE  312.     COM-    arms  expand,  the  loaded  free  ends  a,  a'  of  the 
PENS  AT  ED  BALANCE    sectionsmove  inward,  thus  compensating  for  the 
increased  length  of  the  radial  arms.     The  final 
adjustment  is  made  by  screwing  in  or  out  the  studs  on  the  rim. 

336.  Cubical  Expansion.  —  In  general,  solids  and  liquids 
when  heated  expand  in  all  directions  with  increase  of 
volume.  This  expansion  in  volume  is  called  cubical  ex- 
pansion.  The  coefficient  of  cubical  expansion  is  the  increase 
in  volume  of  a  unit  volume  per  degree  rise  of  temperature. 

Precisely  as  in  the  case  of  linear  expansion,  the  coeffi- 
cient of  cubical  expansion  Jc  may  be  expressed  by  the 
equation 


Whence 

The  coefficient  of  cubical  expansion  of  a  substance  is 
three  times  its  coefficient  of  linear  expansion.  Thus  if 
the  coefficient  of  linear  expansion  of  cast  iron  is  0.0000113, 
its  coefficient  of  cubical  expansion  is  0.0000339. 

337.  Expansion  of  Water.  —  Water  exhibits  the  remark- 
able property  of  contracting  when  heated  at  the  freezing 
point.  This  contraction  continues  up  to  4°  C.,  when  ex- 
pansion sets  in.  The  greatest  density  of  water  is  therefore 
at  4°  C.,  and  its  density  at  6°  is  nearly  the  same  as  at  2°. 


THE  ABSOLUTE  SCALE  293 

In  a  lake  or  pond  water  at  4°  sinks  to  the  bottom,  while 
water  below  4°  is  lighter  and  rises  to  the  top,  where  the 
freezing  begins.  Ice  forms  at  the  surface  of  a  body  of 
cold  water,  which  freezes  from  the  surface  downwards. 
Fishes  are  thus  protected  from  freezing. 

338.  Law   of  Charles.  —  It   was   shown   by   Charles,  in 
>  1787,  that  the  volume  of  a  given  vnass  of  any  gas  under 

constant  pressure  increases  by  a  constant  fraction  of  its 
volume  at  zero  for  each  rise  of  temperature  of  1°  C.  The 
investigations  of  Regnault  and  others  show  that  the  law 
is  not  rigorously  true,  and  that  the  accuracy  of  Charles's 
law  is  about  the  same  as  that  of  Boyle's  law.  The  coeffi- 
cient of  expansion  k  of  dry  air  is  0.003665,  or  about  gy-j. 
This  fraction  may  be  considered  as  the  coefficient  of  ex- 
pansion of  any  true  gas. 

339.  The  Absolute  Scale.  —  The  law  of  Charles  leads  to 
a  scale  of  temperature  called  the  absolute  scale.     By  this 
law  the  volumes  of  any  mass  of  gas,  under  constant  pres- 
sure, at  0°  C.,  and  at  any  other  temperature  t°  C.,  are 
connected  by  the  following  relations  (§  336)  : 


At  any  other  temperature,  tr,  the  volume  becomes 


, 


273 
Divide  (a)  by  (6)  and 

v 


Suppose  now  a  new  scale  is  taken,  whose  zero  is  273 
Centigrade  divisions  below  the  freezing  point  of  water, 


294  HEAT 

and  that   temperatures  on  this   scale  are  denoted   by  T. 
Then  273  +  1  will  be  represented  by  T,  and  273  +  1'  by 


v1     273  +  *'      Tf1 

or  £  he  volumes  of  the  same  mass  of  gas  under  constant  pres- 
sure are  proportional  to  the  temperatures  on  this  new  scale. 
The  point  273°  below  0°  C.  is  called  the  absolute  zero,  and 
the  temperatures  on  this  scale,  absolute  temperatures.  Up 
to  the  present  it  has  not  been  found  possible  to  cool  a 
body  to  the  absolute  zero;  but  by  evaporating  liquid 
hydrogen  under  very  low  pressure,  a  temperature  esti- 
mated to  be  within  9°  of  the  absolute  zero  has  been  ob- 
tained by  Professor  Dewar;  and  Professor  Onnes,  by 
liquefying  helium,  believes  that  he  obtained  a  tempera- 
ture within  2°  or  3°  of  the  absolute  zero. 

At  these  low  temperatures  steel  and  rubber  become  as 
brittle  as  glass. 

340.  The  Gas  Equation.  —  The  laws  of  Boyle  and  Charles 
may  be  combined  into  one  expression,  which  is  known  as 
the  gas  equation.  It  has  a  wider  application  even  than  its 
method  of  derivation  would  indicate. 

Let  v0,  jt?0,  TQ  be  the  volume,  pressure,  and  absolute  tem- 
perature of  a  given  mass  of  gas. 

Also  let  v,  JP,  T  be  the  corresponding  quantities  for  the 
same  mass  of  gas  at  pressure  p  and  temperature  T. 
Then  applying  Boyle's  law  (§  87)  to  increase  the  pres- 
sure to  the  value  p,  the  temperature  remaining  constant, 
we  have 

V*  .......  oo 

v'     pQ 

where  vr  is  the  new  volume  corresponding  to  the  pres- 
sure p. 


QUESTIONS  AND  PROBLEMS  295 

Next  apply  the  law  of  Charles  (§  339),  keeping  the 
pressure  constant  at  the  value  jo,  and  starting  with  the 
new  volume  vf.  Then  since  the  volumes  are  directly 
proportional  to  the  temperatures,  we  have 


<•> 


where  v  is  the  new  volume  corresponding  to  temperature  T. 
Multiply  (a)  and  (5)  together  member  by  member,  and 

^o  —  £±09  or  PA  =  2™.  =  a  constant,  since  p  and  ^Tare  any 

pressure  and  temperature  and  v  corresponds.     This  con- 
stant is  usually  denoted  by  R.     We  may  therefore  write 

pv  =  RT.  .     .     .     (Equation  33) 

To  illustrate  the  use  of  the  above  relation  :  If  20  cm.8  of  gas  'at 
20°  C.  is  under  a  pressure  of  76  cm.  of  mercury,  what  will  be  the 
pressure  when  its  volume  is  30  cm.8  and  temperature  50°  C.? 

From  equation  (33),  ^  is  a  constant, 


or 


273 
from  which 


Questions  and  Problems 

1.  Telegraph  wires  often  "  hum  "  in  the  wind.     Why  is  the  pitch 
higher  in  winter  than  in  summer  ? 

2.  When  a  piece  of  ice  floats,  about  ^  of  its  volume  projects  out 
of  the  water.     If  a  pan  is  level  full  of  water  and  a  piece  of  ice  floats 
in  it,  both  at  0°  C.,  why  is  there  no  change  of  level  when  the  ice 
melts? 

3.  Why  is  a  fountain  pen  more  likely  to  leak  when  nearly  empty  ? 


296  BEAT 

4.  If  the  bulb  of  a  mercurial  thermometer  is  plunged  into  hot- 
water,  the  top  of  the  thread  of  mercury  first  falls  and  then  rises. 
Explain.   ' 

5.  A  copper  rod  125  cm.  long  at  0°  C.  expands  to  125.209  cm.  at 
100°  C.    Find  the  coefficient  of  linear  expansion  of  copper. 

6.  The  coefficient  of  linear  expansion  of  steel  is  0.0000132.    What 
will  be  the  variation  in  length  of  a  steel  bridge  250  ft.  long  between 
the  temperatures  -  10°  C.  and  40°  C.? 

7.  The  coefficient  of  linear  expansion  of  steel  is  0.0000132  and 
that  of  zinc  is  0.0000294.      What  relative  lengths  of  rods  of  these 
metals  will  have  equal  expansions  in  length  for  the  same  changes  of 
temperature  ? 

8.  The  coefficient  of  the  volume  expansion  of  glass  is  0.000258. 
A  density  bottle  at  15°  C.  holds  25  cm.8.     What  will  be  its  capacity 
at25°C.? 

9.  Why  should  the  reading  of  the  mercurial  barometer  be  cor- 
rected for  temperature?    If  the  relative  volume  coefficient  of  expan- 
sion of  mercury  in  glass  is  0.000155,  and  the  barometer  reads  755  mm. 
at  20°  C.,  what  would  be  the  reduced  reading  at  0°  C.  ? 

10.  The  volume  of  a  given  mass  of  gas  at  740  mm.  pressure  is 
1200  cm.8 ;  find  its  volume  at  760  mm. 

11.  The  mass  of  a  liter  of  air  at  0°  C.  and  76  cm.  pressure  is  1.3  g. 
Find  the  mass  of  10  liters  of  air  at  20°  C.  and  74  cm.  pressure. 

12.  A  liter  of  hydrogen  at  15°  C.  is  heated  at  constant  pressure  to 
75°  C.     Find  its  volume. 

13.  A  quantity  of  gas  is  collected  in  a  graduated  tube  over  mer- 
cury.    The  reading  of  the  mercury  level  in  the  tube  is  20  cm.,  the 
volume  of  the  gas  is  60  cm.3,  the  temperature  is  20°  C.,  and  the  ba- 
rometer reading  is  74cm.   How  many  cubic  centimeters  of  gas  are 
there  at  0°  C.  and  76  cm.  pressure? 

14.  Three  cubic  centimeters  of  air  are  introduced  into  the  vacuum 
of  a  mercurial  barometer.     The  barometer  read  76  cm.  before  intro- 
ducing the  air  and  57  cm.  after.     What  volume  does  the  air  occupy  in 
the  barometer  ? 


SPECIFIC  HEAT  297 

IV.   MEASUREMENT  OF  HEAT 

341.  The  Unit  of  Heat.  — The  unit  of  heat  in  the  c.  g.  s. 
system  is  the  calorie.     It  is  defined  as  the  quantity  of  heat 
that  will  raise  the  temperature  of  one  gram  cf  water  one  de- 
gree Centigrade.     There  is  no  agreement  as  to  the  position 
of  the  one  degree  on  the  thermometric  scale,  although  it  is 
known  that  the  unit  quantity  of  heat  varies  slightly  at 
different   points  on   the  scale.      If    the  degree'  interval 
chosen  is  from  15°  to  16°  C.,  the  calorie  is  then  the  one 
hundredth  part  of  the  heat  required  to  raise  the  tempera- 
ture of  one  gram  of  water  from  0°  to  100°  C. 

In  engineering  practice  in  England  and  America  the 
British  thermal  unit  (B.  T.  U.)  is  commonly  employed.  It 
is  the  heat  required  to  raise  the  temperature  of  one  pound 
of  water  one  degree  Fahrenheit. 

342.  Thermal  Capacity.  —  The  thermal  capacity  of  a  body 
is  the  number  of  calories  required  to  raise  its  temperature 
one  degree  Centigrade.     The  thermal  capacity  of  equal 
masses  of  different  substances  differs  widely.    For  example, 
if  100  g.  of  water  at  0°  C.  be  mixed  with  100  g.  at  100°  C., 
the  temperature  of  the  whole  will  be  very  nearly  50°.  C. 
But  if  100  g.  of  copper  at  100°  C.  be  cooled  in  100  g.  of 
water  at  0°  C.,  the  final  temperature  will  be  about  9.1°  C. 
The  heat  lost  by  the  copper  in  cooling  through  90.9°  is 
sufficient  to  heat  the  same  mass  of  water  only  9.1°,  that  is, 
the  thermal  capacity  of  water  is  about  ten  times  as  great 
as  that  of  an  equal  mass  of  copper. 

343.  Specific  Heat.  —  The  specific  heat  of  a  substance  is 
the  number  of  calories  of  heat  required  to  raise  the  tem- 
perature of  one  gram  of  it  through  one  degree  Centigrade. 
It  may  be  defined  independently  of  any  temperature  scale 
as  the  ratio  between  the  number  of  units  of  heat  required 


298  HEAT 

to  raise  the  temperature  of  equal  masses  of  the  substance 
and  of  water  through  one  degree.  The  specific  heat  of 
mercury  is  0.033,  that  is,  the  heat  that  will  raise  1  g.  of 
mercury  through  1°  C.  will  raise  1  g.  of  water  through 
only  0.033°  C. 

The  specific  heat  of  water  is  twice  as  great  as  that  of  ice 
(0.505),  and  more  than  twice  as  great  as  that  of  steam 
under  constant  pressure  (0.477). 

344.  Numerical  Problem  in  Specific  Heat.  —  The  principle  ap- 
plied in  the  solution  of  such  problems  is  that  the  gain  or  loss  of  heat 
by  the  water  is  equal  to  the  loss  or  gain  of  heat  by  the  body  introduced 
into  the  water.  The  gain  or  loss  of  heat  by  the  body  is  equal  to  the 
product  of  its  mass,  its  specific  heat,  and  its  change  of  temperature. 

To  illustrate :  20  g.  of  iron  at  98°  C.  are  placed  in  75  g.  of  water  at 
10°  C.  contained  in  a  copper  beaker  weighing  15  g.,  specific  heat  0.095. 
The  resulting  temperature  of  the  water  and  the  iron  is  12.5°  C.  Find 
the  specific  heat  of  iron. 

The  thermal  capacity  of  the  beaker  is  15  x  0.095  =  1.425  calories. 
The  heat  lost  by  the  iron  is  20  x  s  x  (98  —  12.5)  calories,  in  which  s 
represents  the  specific  heat  of  iron,  and  (98  —  12.5)  its  change  of  tem- 
perature. The  heat  gained  by  the  water  and  the  copper  vessel  is  (75  + 
1.425)  x  (12.5  —  10)  calories  ;  the  second  factor  is  the  gain  in  temper- 
ature of  the  water  and  the  beaker.  It  follows  by  equating  these  two 
quantities  that  20  x  s  x  (98  -  12.5)  =  (75  +  1.425)  x  (12.5  -  10). 
Solving  for  s,  we  have  s  =  0.112  calorie  per  gram. 

Questions  and  Problems 

1.  What  is  the  specific  heat  of  water? 

2.  A  pound  of  water  and  a  pound  of  lead  are  subjected  to  the 
same  source  of  heat  for  10  inin.     Which  will  be  at  the  higher  tem- 
perature ? 

3.  If  equal  quantities  of  heat  are  applied  to  equal  masses  of  iron 
and  lead,  which  will  show  the  greater  change  of  temperature  ? 

4.  Equal  balls  of  iron  and  zinc  are  heated  in  boiling  water  and 
are  placed  on  a  cake  of  beeswax.     Which  will  melt  the  further  into 
the  wax  ? 


THE  MELTING  POINT  299 

5.  Why  is  water  better  than  any  other  liquid  for  heating  purposes  ? 

6.  Why  is  a  rubber  bag  filled  with  hot  water  better  for  a  foot 
warmer  than  an  equal  mass  of  any  solid  ? 

7.  A  copper  beaker  has  a  mass  of  25  g.     The  specific  heat  of  cop- 
per is  0.095.     What  is  the  thermal  capacity  of  the  beaker  ? 

8.  How  much  heat  will  it  take  to  raise  a  liter  of  water  from  20°  C. 
to  100°  C.? 

9.  The  specific  heat  of  iron  is  0.112.     How  much  heat  will  be  re- 
quired to  raise  250  g.  of  iron  from  10°  to  45°  C.  ? 

10.  120  g.  of  water  at  5°  C.  are  mixed  with  200  g.  of  water  at  50°  C. 
Assuming  that  no  heat  is  lost,  what  will  be  the  resulting  temperature? 

11.  89.2  g.  of  iron  at  90°  C.  are  placed  in  70  g.  of  water  at  10°  C. ; 
the  resulting  temperature  is  20°  C.     Find  the  specific  heat  of  iron. 

12.  A  copper  ball  weighing  1  kg.  has  a  specific  heat  of  0.095.     It 
is  heated  in  a  furnace  to  the  temperature  of  the  furnace  and  dropped 
into  a  liter  of  water  at  10°  C.     The  temperature  of  the  water  rises  to 
93.1°  C.     Find  the  temperature  of  the  furnace. 

13.  How  many  calories  in  the  British  Thermal  Unit  ? 

14.  A  glass  beaker  weighs  100  g.     If  the  specific  heat  of  the  glass 
is  0.177,  how  much  water  will  have  the  same  thermal  capacity  as  the 
beaker? 

15.  Why  do  islands  in  the  sea  have  smaller  extremes  of  temperature 
than  inland  areas  ? 

V.   CHANGE  OF  STATE 

345.  The  Melting  Point.  —  A  body  is  said  to  melt  or  fuse 
when  it  changes  from  the  solid  to  the  liquid  state  by  the 
application  of  heat.  The  change  is  called  melting,  fusion, 
or  liquefaction.  The  temperature  at  which  fusion  takes 
place  is  called  the  melting  point.  Solidification  or  freezing 
is  the  converse  of  fusion,  and  the  temperature  of  solidifi- 
cation is  usually  the  same  as  the  melting  point  of  the 
same  substance.  Water,  if  undisturbed,  may  be  cooled  a 
.number  of  degrees  below  0°  C.,  but  if  it  is  disturbed  it 


300  HEAT 

usually  freezes  at  once,  and  its  temperature  rises  to  the 
freezing  point. 

The  melting  point  of  crystalline  bodies  is  well  marked. 
A  mixture  of  ice  and  water  in  any  relative  proportion 
will  remain  without  change  if  the  temperature  of  the  room 
is  0°  C. ;  but  if  the  temperature  is  above  zero,  some  of  the 
ice  will  melt;  if  it  is  below  zero,  some  of  the  water  will 
freeze.  Some  substances,  like  wax,  glass,  and  wrought 
iron,  have  no  sharply  defined  melting  point.  They  first 
soften  and  then  pass  more  or  less  slowly  into  the  condition 
of  a  viscous  liquid.  It  is  this  property  which  permits  of 
the  bending  and  molding  of  glass,  and  the  rolling,  welding, 
and  forging  of  iron. 

346.   Change  in  Volnme  accompanying  Fusion.  —  Fit  to  a 

small  bottle  a  perforated  stopper  through  which  passes  a  fine  glass 
tube.  Fill  with  water  recently  boiled  to  expel  the  air,  the  water  ex- 
tending halfway  up  the  tube.  Pack  the  apparatus  in  a  mixture  of 
salt  and  finely  broken  ice.  The  water  column  at  first  will  fall  slowly, 
but  in  a  few  minutes  it  will  begin  to  rise,  and  will  continue  to  do  so 
until  water  flows  out  of  the  top  of  the  tube.  The  water  in  the  bottle 
freezes,  expands,  and  causes  the  overflow. 

Most  substances  occupy  a  larger  volume  in  the  liquid 
state  than  in  the  solid;  that  is,  they  expand  in  liquefying. 
A  few  substances,  like  water  and  bismuth,  expand  in 
solidifying.  '  When  water  freezes,  its  volume  increases 
9  per  cent.  If  this  expansion  is  resisted,  water  in  freezing 
is  capable  of  exerting  a  force  of  about  2000  kg.  per 
square  centimeter.  This  explains  the  bursting  of  water 
pipes  when  the  water  in  them  freezes,  and  the  rending  of 
rocks  by  the  freezing  of  water  in  cracks  and  crevices.  The 
expansion  of  cast  iron  and  type  metal  when  they  solidify 
accounts  for  the  exact  reproduction  of  the  mold  in  which 
they  are  cast. 


BEAT  OF  FUSION 


301 


347.  Effect  of  Pressure  on  the  Melting  Point.  —  Support  a 

rectangular  block  or  prism  of  ice  on  a  stout  bar  of  wood.  Pass  a 
thin  iron  wire  around  the  ice  and  the  bar  of  wood,  and  suspend  on  it 
a  weight  of  25  to  50  Ib.  The  pressure  of  the  wire  lowers  the  melting 
point  of  the  ice  immediately  under  it  and  the  ice  melts ;  the  water, 
after  passing  around  the  wire,  where  it  is  relieved  of  pressure,  again 
freezes.  In  this  way  the  wire  passes  slowly  through  the  ice,  leaving 
the  block  solidly  frozen. 

A  rough  numerical  statement  of  the  effect  of  pressure 
on  the  freezing  point  of  water  is  that  a  pressure  of  one 
ton  per  square  inch  lowers  the  freezing  point  to  —  1°  C. 
Familiar  examples  of  refreezing,  or  regelation,  are  the 
hardening  of  snowballs 
under  the  pressure  of 
the  hands,  the  formation 
of  solid  ice  in  a  roadway 
where  it  is  compressed 
by  vehicles  and  the  hoofs 
of  horses,  and  frozen 
footforms  in  compact  ice 
after  the  loose  snow  has 
melted  around  them. 
The  ice  of  a  glacier  melts 
where  it  is  under  the 
enormous  pressure  of 

the  descending  masses  F|CURE  3,3. -MERDE  GLACE,  CHAMOUN.X. 
above  it.  The  melting 

permits  the  ice  to  accommodate  itself  to  abrupt  changes 
in  the  rocky  channel,  and  a  slow  iceflow  results.  As  soon 
as  the  pressure  at  any  surface  is  relieved,  the  water  again 
freezes  (Fig.  313). 

348.  Heat  of  Fusion.  —  When  a  solid  melts,  a  quantity 
of  heat  disappears  ;   and,  conversely,  when  a  liquid  solidi- 
fies, the  amount   of   heat  generated  is  the  same    as  dis- 


302  HEAT 

appears  during  liquefaction.  The  heat  of  fusion  of  a 
substance  is  the  number  of  calories  required  to  melt  a 
gram  of  it  without  change  of  temperature.  The  heat  of 
fusion  of  ice  is  80  calories. 

As  an  illustration  of  the  heat  of  fusion,  place  200  g.  of  clean  ice, 
broken  into  small  pieces,  into  500  g.  of  water  at  60°  C.  When  the 
ice  has  melted,  the  temperature  will  be  about  20°  C.  The  heat  lost 
by  the  500  g.  of  water  equals  500  x  (60  -  20)  =  20,000  calories.  This 
heat  goes  to  melt  the  ice  and  to  raise  the  resulting  water  from  0°  C.  to 
20°  C.  To  raise  this  water  from  0°  to  20°  requires  200  x  20  =  4000 
calories.  The  remainder,  20,000  -  4000  =  16,000  calories,  went  to 
melt  the  ice.  Then  the  heat  of  fusion  of  ice  is  16,000  -r-  200  =  80 
calories  per  gram. 

349.  Heat  lost  in  Solution.  —  Fill  a  beaker  partly  full  of  water 
at  the  temperature  of  the   room,  and  add  some  ammonium   nitrate 
crystals.   The  temperature  of  the  water  will  fall  as  the  crystals  dissolve. 

This  experiment  illustrates  the  fact  that  heat  disap- 
pears when  a  body  passes  from  the  solid  to  the  liquid 
state  by  solution.  The  use  of  salt  in  soup  or  of  sugar 
in  tea  absorbs  heat.  The  heat  energy  is  used  to  pull 
down  the  solid  structure. 

350.  Freezing  Mixtures.  —  Freezing  mixtures  are  based 
on  the  absorption  of  heat  necessary  to  give  fluidity.     Salt 
water  freezes  at   a  lower  temperature  than  fresh  water. 
When  salt  and  snow  or  pounded  ice  are  mixed  together, 
both  become  fluid  and  absorb  heat  in  the  passage  from 
the  one  state  to  the  other.     By  this  mixture  a  tempera- 
ture of  —  22°  C.  may  be  obtained.     Still  lower  tempera- 
tures may  be  reached  with  other  mixtures,  notably  with 
sulpho-cyanide  of  sodium  and  water. 

351.  Vaporization.  —  Pour  a  few  drops  of  ether  into  a  beaker 
and  cover  closely  with  a  plate  of  glass.     After  a  few  seconds  bring 
a  lighted  taper  to  the  mouth  of  the  beaker.     A   sudden  flash  will 
show  that  the  vapor  of  ether  was  mixed  with  the  air. 


COLD  BY  EVAPORATION  303 

Support  on  an  iron  stand  a  Florence  flask  two-thirds  full  of  water 
and  apply  heat.  In  a  short  time  bubbles  of  steam  will  form  at  the 
bottom  of  the  flask,  rise  through  the  water,  and  burst  at  the  top,  pro- 
ducing violent  agitation  throughout  the  mass. 

Vaporization  is  the  conversion  of  a  substance  into  the 
gaseous  form.  If  the  change  takes  place  slowly  from 
the  surface  of  a  liquid,  it  is  called  evaporation  ;  but  if  the 
liquid  is  visibly  agitated  by  rapid  internal  evaporation, 
the  process  is  called  ebullition  or  boiling. 

352.  Sublimation.  —  When  a   substance   passes  directly 
from    the    solid   to   the    gaseous    form   without   passing 
through  the  intermediate  state  of  a  liquid,  it  is  said  to 
sublime.     Arsenic,  camphor,  and  iodine  sublime  at  atmos- 
pheric  pressure,    but  if   the  pressure   be   sufficiently  in- 
creased, they  may  be  fused.     Ice  also  evaporates  slowly 
even   at  a   temperature  below  freezing.     Frozen  clothes 
dry  in  the  air  in  freezing  weather.     At  a  pressure   less 
than  4.6  mm.  of  mercury,  ice  is  converted  into  vapor  by 
heat  without  melting. 

353.  The  Spheroidal  State.  —  When  a  small  quantity  of 
liquid  is  placed  on  hot  metal,  as  water  on  a  red-hot  stove, 
it  assumes  a  globular  or  spheroidal  form,  and  evaporates 
at  a  rate  between  ordinary  evaporation  and  boiling.     It 
is   then   in  the   spheroidal   state.     The  vapor  acts  like  a 
cushion  and  prevents  actual  contact  between  the  liquid 
and  the  metal.     The  globular  form  is  due  to  surface  ten- 
sion.    Liquid  oxygen  at  —  180°  C.  assumes  the  spheroidal 
form  on  water.     The  temperature  of   the  water  is  rela- 
tively high   compared  with   that   of  the  liquid   oxygen. 

354.  Cold  by  Evaporation.  —  Tie  a  piece  of  fine  linen  around  the 
bulb  of  a  thermometer  and  pour  on  it  a  few  drops  of  sulphuric  ether. 
The  temperature  will  at  once  begin  to  fall,  showing  that  the  bulb 
has  been  cooled. 


304 


HEAT 


In  the  evaporation  of  ether,  some  of  the  heat  of  the 
thermometer  is  used  to  do  work  on  the  liquid. 

Sprinkling  the  floor  of  a  room  cools  the  air,  because  of 
the  heat  expended  in  evaporating  the  water.  Porous 
water  vessels  keep  the  water  cool  by  the  evaporation  of 
the  water  from  the  outside  surface.  Liquid  carbon 
dioxide  is  readily  frozen  by  its  own  rapid  evaporation. 
Dewar  liquefied  oxygen  by  means  of  the  temperature 
obtained  through  the  successive  evaporation  of  liquid 
nitrous  oxide  and  ethylene.  Similarly,  by  the  evapora- 
tion of  liquid  air  he  has  liquefied  hydrogen.  The  evapo- 
ration of  liquid  hydrogen  under  reduced  pressure  has 


'I1  To  Sewer  —Regulating  Valve 

FIGURE  314.  — ICE  PLANT. 

enabled  him  to  obtain  a  temperature  but  little  removed 
from  the  absolute  zero,  —  273°  C.  More  recently  Pro- 
fessor Onnes  of  Leyden,  by  the  evaporation  of  liquid 
helium,  has  reached  the  extremely  low  temperature  of 
-271.3°  C.  or  1.7°  absolute. 

355.  Ammonia  Ice  Plant.  —  The  low  temperature  produced  by 
the  rapid  evaporation  of  liquid  ammonia  is  utilized  in  the  manufac- 
ture of  ice  and  for  general  cooling  in  refrigerator  plants.  Ammonia 
may  be  liquefied  by  pressure  alone.  At  a  temperature  of  80°  F.  the 


EFFECT  OF  PRESSURE  ON   THE  BOILING  POINT     305 


required  pressure  is  155  pounds  per  square  inch.  The  essential  parts 
of  an  ice  plant  are  shown  in  Fig.  314.  Gaseous  ammonia  is  com- 
pressed by  a  pump  in  condenser  pipes,  over  which  flows  cold  water  to 
remove  the  heat.  From  the  condenser  the  liquid  ammonia  passes 
very  slowly  through  a  regulating  valve  into  the  pipes  of  the  evapo- 
rator. The  pressure  in  the  evaporator  is  kept  low  by  the  pump,  which 
acts  as  an  exhaust  pump  on  one  side  and  as  a  compressor  on  the  other. 
The  pump  removes  the  evaporated  ammonia  rapidly  and  the  evapora- 
tion absorbs  heat.  The  pipes  in  which  the  evaporation  takes  place 
are  either  in  a  tank  of  brine,  or  in  the  refrigerating  room.  Smaller 
tanks  of  distilled  water  are  placed  in  the  brine  until  the  water  in 
them  is  frozen.  The  pipes  in  the  refrigerating  room  are  covered  with 
hoar  frost,  which  is  frozen  moisture  from  the  air.  The  temperature  of 
the  brine  is  reduced  to  about  16°  to  18°  F. 
The  brine  does  not  freeze  at  this  tempera- 
ture. 

The  process  is  continuous  because  the 
gaseous  ammonia  is  returned  to  the  con- 
densing coils,  which  are  cooled  with  water. 
It  thus  passes  repeatedly  through  the  same 
cycle  of  physical  changes. 

356.  Effect  of  Pressure  on  the  Boil- 
ing Point.  —  Place  a  flask  of  warm  water 
under  the  receiver  of  an  air  pump.  It 
will  boil  violently  when  the  receiver  is  ex- 
hausted* 

Fill    a    round-bottomed    Fj^rence    flask 
half  full  of  water  and  heat  until  it  boils 
vigorously.     Cork  the  flask,  invert,  and  sup- 
port it  on  a  ring  stand  (Fig.  315).     The  boiling  ceases,  but  is  re- 
newed by  applying  cold  water  to  the  flask.     The  cold  water  condenses 
the  vapor,  and  reduces  the  pressure  within  the  flask  so  that  the  boil- 
ing begins  again. 

The  effect  of  pressure  on  the  boiling  point  is  seen  in 
the  low  temperature  of  boiling  water  at  high  elevations, 
and  in  the  high  temperature  of  the  water  under  pressure 
in  digesters  used  for  extracting  gelatine  from  bones.  The 
boiling  point  of  water  falls  1°  C.  for  an  increase  in  eleva- 


FIGURE  315.  —  BOILING 
UNDER  REDUCED  PRESSURE. 


306 


HEAT 


tion  of  about  295  in.     At  Quito  the  boiling  point  is  near 
90°  C. 

357.  Heat  of  Vaporization.  —  The  heat  of  vaporization  is 
the  number  of  calories  required  to  change  one  gram  of  a 
liquid  at  its  boiling  point  into  vapor  at  the  same  tempera- 
ture.    Water  has  the  greatest  heat  of  vaporization  of  all 
liquids.     The  most  carefully  conducted  experiments  show 
that  the  heat  of  vaporization  of  water  under  a  pressure  of 

one  atmosphere  is  536.6  calo- 
ries per  gram. 

Set  up  apparatus  like  that  shown 
in  Tig.  316.  The  steam  from  the 
boiling  water  is  conveyed  into  a 
beaker  containing  a  known  quantity 
of  water  at  a  known  temperature. 
The  increase  in  the  mass  of  water 
gives  the  amount  of  steam  con- 
densed. The  "  trap  "  in  the  delivery 
tube  catches  the  water  that  condenses 
before  it  reaches  the  beaker.  Sup- 
pose that  the  experiment  gave  the 
following  data:  Amount  of  water 
in  the  beaker,  400  g.  at  the  begin- 
ning, 414.1  g.  at  the  end,  including 
the  thermal  capacity  of  the  beaker 
in  terms  of  water  ;  temperature  at  the  beginning,  20°  C.,  and  at  the 
end,  41°  C. ;  observed  boiling  point,  99°  C. ;  there  were  14.1  g.  of 
steam  condensed.  Now,  by  the  principle  that  the  heat  lost  or  given 
off  by  the  steam  equals  that  gained  by  the  water,  we  have 

400  x  (41  -  20)  =  14.1  x  /  +  14.1  x  (99  -  41)  ; 
whence  I  =  537.7  cal.  per  gram. 

358.  Formation  of  Dew. — The  presence  of  clouds  and  the 
"  sweating  "  of  pitchers  filled  with  ice  water  show  that  the 
atmosphere  contains  water  vapor.     The  amount  of  water 


FIGURE  316.  —  HEAT  OF 
EVAPORATION. 


HUMIDITY  AND  HEALTH  307 

vapor  that  the  atmosphere  can  hold  in  suspension  depends 
on  its  temperature.  After  sunset,  if  the  sky  is  clear,  bodies 
on  the  earth's  surface,  such  as  grass,  leaves,  and  roots,  soon 
cool  below  the  temperature  of  the  surrounding  air,  and 
water  in  the  form  of  dew  collects  on  them.  Clouds  act  as 
blankets  and  prevent  the  cooling  off  process,  so  that  little 
or  no  dew  collects.  Wind  promotes  evaporation  and  dew 
fails  to  collect.  If  the  temperature  falls  sufficiently  low, 
the  dew  is  deposited  as  frost. 

359.  The  Dew  Point.  —  The  dew  point  is  the  temperature 
at  which  the  aqueous  vapor  of  the  atmosphere  begins  to  con- 
dense.    If  water  at  the  temperature  of  the  room  be  poured 
into  a  polished  nickel-plated  beaker  and  small  pieces  of  ice 
be  added  with  stirring,  a  mist  will  soon  collect  on  the  out- 
side of  the  beaker.     The  temperature  of  the  water  is  then 
the  dew  point. 

360.  Humidity.  —  The  terms  dryness  and  moisture  ap- 
plied to  the  air  are  purely  relative.     Usually  the  air  is  not 
saturated,  that  is,  it  does  not  contain  all  the  water  vapor 
it  can  hold.     If  it  is  near  the  saturation  point,  it  is  moist; 
if  it  is  very  far  from  saturation,  it  is  dry.     The  relative 
humidity  of  the  air  is  the  ratio  between  the  amount  of  water 
vapor  actually  present  and  the  amount  that  would  be  present 
if  the  air  were  saturated  at  the  same  temperature.     The  air 
is  saturated  at  the  dew  point.     A  dry  day  is  one  on  which 
the  dew  point  is  much  below  the  temperature  of  the  air ; 
a  damp  day  is  one  on  which  the  dew  point  is  close  to  the 
temperature  of  the  air.     Humidity  is  expressed  as  a  per 
cent  of  saturation. 

361.  Humidity  and  Health. —The  humidity  of  the  air 
has  an  important  bearing  on  health.     The  dry  air  of  a 
furnace-heated  house  promotes  excessive  evaporation  from 
the  bodies  of  the  occupants,  producing  sensations  of  chil- 


308  HEAT 

liness  and  discomfort.  On  the  other  hand,  excessive 
humidity  retards  healthful  evaporation,  gives  a  sensation 
of  depression,  and  in  hot  weather  checks  Nature's  method 
of  keeping  cool  by  evaporation.  The  humidity  conducive 
to  health  is  about  50  per  cent. 

Questions  and  Problems 

1.  Why  does  a  drop  of  alcohol  on  the  hand  feel  cold? 

2.  Why  does  a  shower  in  summer  cool  the  air? 

3.  Why  is  there  less  dew  on  gravel  than  on  the  grass? 

4.  Why  can  blocks  of  ice  be  made  to  adhere  by  pressure? 

5.  Why  do  your  eye  glasses  fog  over  when  you  go  from  the  cold 
air  outside  into  a  warm  room  ? 

6.  Water  in  a  porous  vessel  standing  in  a  current  of  air  is  colder 
than  water  in  a  glass  pitcher.     Why? 

7.  Why  does  warming  a  room  make  it  feel  dryer  ? 

8.  Why  does  water  boil  away  faster  on  some  days  than  on  others? 

9.  Why  does  wind  dry  up  the  roads  after  a  rain? 

10.  Why  does   moisture   collect  on  the   carburetor  of   a  gasoline 
engine  when  it  is  in  operation  unless  it  is  heated? 

11.  How  much  heat  does  it  take  to  convert  50  g.  of  water  at  100° 
C.  into  steam  at  100°  C.? 

12.  How  much  ice  will  100  g.  of  water  at  100°  C.  rnelt? 

13.  How  much  ice  will  100  g.  of  steam  at  100°  C.  melt? 

14.  100  g.  of  ice  and  20  g.  of  steam  at  100°  C.  are   put   into   a 
calorimeter.     If  no  heat  is  lost,  what  will  be  the  temperature  of  the 
water  after  all  the  ice  is  melted  ? 

15.  How  much  water  at  80°  C.  will  just  melt  a  kilogram  of  ice? 

16.  How  much  steam  will  be  required  to  raise  the  temperature 
of  a  kilogram  of  water  from  20°   to  50°  C.  ? 

17.  How  much  ice  will  it  take  to  cool  a  kilogram  of  water  from 
50°  to  20°  C.  ? 

18.  Mt.  Washington  is  6288  ft.  above  sea  level;  at  what  tempera- 
ture does  water  boil  on  its  top  ? 


CONDUCTION  309 

19.  Water  boils  in  the  City  of  Mexico  at  92.3°  C.     What  is  its 
elevation  above  the  sea  ? 

20.  50  g.  of  ice  at  0°  C.  are  put  into  50  g.  of  water  at  35°  C.     How 
much  of  the  ice  will  melt  ? 

VI.    TRANSMISSION   OF   HEAT 

362.    Conduction.  —  Twist  together  two  stout  wires,  iron  and  cop- 
per, of  the  same  diameter,  forming  a  fork,  with  long  parallel  prongs 


FIGURE  317.  —  DIFFERENCE  IN  CONDUCTIVITY. 

and  a  short  stem.  Support  them  on  a  wire  stand  (Fig.  317),  and  heat 
the  twisted  ends.  After  several  minutes  find  the  point  on  each  wire, 
farthest  from  the  flame,  where  a  sulphur  match  ignites  when  held 
against  the  wire.  This  point  will  be  found  farther  along  on  the  cop- 
per than  on  the  iron,  showing  that  the  former  has  led  the  heat  farther 
from  its  source. 

Prepare  a  cylinder  of  uniform  diameter,  naif  of  which  is  made  of 
brass  and  half  of  wood.  Hold  a  piece  of  writing  paper  firmly  around 
the  junction  like  a  loop  (Fig.  318).  By  applying  a  Bunsen  flame  the 
paper  in  contact  with  the  wood  is  soon 
scorched,  while  the  part  in  contact  with 
the  brass  is  scarcely  injured.  The  metal 
conducts  the  heat  away  and  keeps  the 
temperature  of  the  paper  below  the 
point  of  ignition.  The  wood  is  a  poor 
conductor. 

These  experiments  show  that 
solids  differ  in  their  conductivity    FIOURE  3 ,  g'J^IL  HALF 
for  heat.     The  metals  are  the  best  WOOD,  HALF  BRASS. 


310 


HEAT 


conductors  ;  wood,  leather,  flannel,  and  organic  substances 
in  general  are  poor  conductors-;  so  also  are  all  bodies  in  a 
powdered  state,  owing  doubtless  to  a  lack  of  continuity  in 
the  material. 

363.  Conductivity  of  Liquids.  —  Pass  a  glass  tube  surmounted 
with  a  bulb  through  a  cork  fitted  to  the  neck  of  a  large  funnel.  Sup- 
port the  apparatus  as  shown  in  Fig.  319. 
The  glass  stem  should  stand  in  colored 
water.  Heat  the  bulb  slightly  to  expel 
some  air,  so  that  the  liquid  will  rise  in  the 
tube.  Fill  the  funnel  with  water,  covering 
the  bulb  to  the  depth  of  about  one  centi- 
meter. Pour  a  spoonful  of  ether  on  the 
water  and  set  it  on  fire.  The  steadiness 
of  the  index  shows  that  little  if  any  of  the 
heat  due  to  the  burning  ether  is  conducted 
to  the  bulb. 

This  experiment  shows  that  water 
is  a  poor  conductor  of  heat.  This 
is  equally  true  of  all  liquids  except 
molten  metals. 

364.  Conductivity  of  Gases.  —  The 
conductivity  of  gases  is  very  small, 
and  its  determination  is  very  diffi- 
cult because  of  radiation  and  convection.  The  conduc- 
tivity of  hydrogen  is  about  7.1  times  that  of  air,  while  the 
conductivity  of  water  is  25  times  as  great. 

365.  Applications  of  Conductivity.  —  If  we  touch  a  piece  of 
marble  or  iron  in  a  room,  it  feels  cold,  while  cloth  and  wood  feel  dis- 
tinctly warmer.  The  explanation  is  that  the  articles  which  feel  cold 
are  good  conductors  of  heat  and  carry  it  away  from  the  hand,  while 
the  poor  conductors  do  not. 

The  good  heat-conducting  property  of  copper  or  brass  is  turned  to 
practical  account  in  Sir  Humphry  Davy's  miner's  lamp  (Fig.  320). 


FIGURE  319.— WATER  POOR 
CONDUCTOR. 


APPLICATIONS   OF  CONDUCTIVITY 


311 


The  flame  is  completely  inclosed  in  metal  and  fine  wire  gauze.  The 
gauze  by  conducting  away  heat  keeps  any  fire  damp  outside  the  lamp 
below  the  temperature  of  ignition  and  so  prevents  ex- 
plosions. The  action  of  the  gauze  is  readily  illustrated 
by  holding  it  over  the  flame  of  a  Bunsen  burner  (Fig. 
321).  The  flame  does  not  pass  through  unless  the  gauze 
is  heated  to  redness.  If  the  gas  is  first  allowed  to  stream 
through  the  gauze,  it  may  be  lighted  on  top  without 
being  ignited  below. 

The  handles  on  metal  instruments 
that  are  to  be  heated  are  usually  made 
of  some  poor  conductor,  as  wood,  bone, 
etc. ;  or  else  they  are  insulated  by  the 
insertion  of  some  non-conductor,  as  in 
the  case  of  the  handles  to  silver  tea- 
pots, where  pieces  of  ivory  are  inserted 
to  keep  them  from  becoming  too  hot. 

The  non-conducting  character  of  air       FlGU*E  320. 
is  utilized  in  houses  with  hollow  walls,    * 
in  double  doors  and  double  windows, 
and  in  clothing  of  loose  texture.     The  warmth  of 
woolen  articles  and  of  fur  is  due  mainly  to  the  fact 
that   much    air    is   inclosed 
within  them  on  account  of 
their  loose  structure. 


FIGURE  32 1 .  — 
FLAME  STOPPED 
BY  WIRE  GAUZE. 


Thermos  Patent 
Reinforcements 


Shook  Absorber 


The  thermos  bottle  consists  of  a  glass  bottle 
with  double  walls  (Fig.  322).  The  space  be- 
tween the  two  walls  is  exhausted  of  air,  and 
the  inner  walls  of  this  vacuum  are  silvered 
to  lessen  radiation  from  one  to  the  other. 
Either  hot  or  cold  liquids  may  be  kept  in  a 
thermos  bottle  with  little  change  of  tempera- 
ture for  several  hours. 

The  "Jireless  cooker  "  is  a  box  of  wood  or 
steel  with  a  metallic  vessel  inside.  The  two 
are  separated  by  heavy  felt  or  other  poorly 
conducting  material  (Fig.  323).  After  the 
material  to  be  cooked  has  been  raised  to  the  proper  temperature,  it  is 
placed  in  the  cooker  and  the  latter  is  tightly  closed.  The  high  tem- 


FIGURE  322.  -THERMOS 
BOTTLE. 


312 


HEAT 


perature  is  maintained  for  three  hours  with  a  drop  of  not  more  than 
10°  or  15°  C.  The  cooking  may  be  completed  without  further  appli- 
cation of  heat.  The  conductivity  of  the  lining  and  of  the  inclosed 

air  is  so  low  that  heat  escapes 
very  slowly.  Additional  heat  is 
often  supplied  by  means  of  hot 
soapstone  or  cast  iron  disks. 

366.  Convection.  —  Set  up 
apparatus  as  shown  in  Fig.  324, 
and  support  it  on  a  heavy  iron 
stand.  Fill  the  flask  and  connect- 
ing tubes  with  water  up  to  a 
point  a  little  above  the  open  end 
of  the  vertical  tube  at  C.  Apply 
a  Bunsen  flame  to  the  flask  B.  A 
circulation  of  water  is  set  up  in 


FIGURE  323.  —  FIRELESS  COOKER. 


the  apparatus,  as  shown  by  the  arrows.     The  circulation  is  made  visible 
by  coloring  the  water  in  the  reservoir  blue  and  that  in  the  flask  red. 

The  process  of  conveying  heat  by  the  transference  of 
the  heated  matter  itself  is  known  as  convection.  Currents 
set  up  in  this  manner  are  called  convection  currents. 

367.  Heating  by  Hot  Water.  —  The  heating 
of  buildings  by  hot  water  conveyed  by  pipes 
to  the  radiators  and  thence  back  again  to  the 
heater  in  the  basement  is  an  application  of 
convection  by  liquids  (Fig.  325).     The  hot 
water  pipe  extends  to  an  open  tank  at  the 
top  of  the  building  to  allow  for  expansion. 
The  circulation  is  maintained  because  the  hot 
water  in  the  pipes  leading  to  the  radiators  is 
hotter  and  therefore  Blighter  than  the  cooler 
water   in  the  return  pipes   beyond   the  ra- 
diators. 

368.  The  Hot  Water  Heater.  —  The  simplest 
arrangement  for  heating  water  for  general    CURRENTS. 


CONVECTION  IN   GASES 


313 


domestic  purposes  is  shown 
in  Fig.  326.  The  cold  water 
enters  the  tank  at  the  top 
through  a  pipe  which  reaches 
nearly  to  the  bottom.  The 
pipe  in  the  bottom  leads  to 
a  heating  coil  in  the  gas 
heater.  The  hot  water  rises 
and  enters  the  tank  at  or 
near  the  top,  while  heavier 
cold  water  takes  its  place 
in  the  heating  coils.  The 
circulation  thus  set  up  con- 
tinues as  long  as  heat  is 
applied. 

369.   Convection  in  Gases.  — 

Set  a  short  piece  of  lighted  candle 
in  a  shallow 
beaker  and 
place  over 
it  a  lamp 
chimney  FlGURE  325.— HEATING  BY  HOT  WATER. 

Pour  into  the  beaker  enough  water  to  close  the 
lower  end  of  the  chimney.  Place  in  the  top  of 
the  chimney  a  T-shaped  piece  of  tin  as  a  short 
partition  (Fig.  327).  If  a  piece  of  smoldering 
paper  be  held  over  one  edge  of  the  chimney,  the 
smoke  will  pass  down  one  side  of  the  partition 
and  up  the  other.  If  the  partition  be  removed, 
the  flame  will  usually  go  out. 

Convection  currents  are  more  easily 
set  up  in  gases  than  in  liquids.      Convec- 
FIGURE  326  "WATER    tion  currents  of  air  on  a  large  scale  are 
HEATER.  present  near  the  seacoast.     The  wind  is 


314 


HEAT 


FIGURE  327.  —  CONVECTION  IN 
GASES. 


a  sea  breeze  during  the  day,  because  the  air  moves  in  from 

the  cooler  ocean  to  take  the  place  of  the  air  rising  over  the 

heated  land.  As  soon  as  the  sun 
sets,  the  ground  cools  rapidly  by 
radiation,  and  the  air  over  it  is 
cooler  than  over  the  sea.  Hence 
the  reversal  in  the  direction  of 
the  wind,  which  is  now  a  land 
breeze. 

370.  Heating  and  Ventilating  by 
Hot  Air.  —  The  hot  air  furnace 
in  the  basement  is  a  heater  for 
burning  wood,  coal,  distillate,  or 
gas,  and  surrounded  by  a  jacket 
of  galvanized  iron  (Fig.  328). 
Cold  air  from  outside  is  heated 
between  the  heater  and  the  jacket 

and  rises  through  the  hot  air  flues  to  registers  in  the  rooms 

of  the  building.     In  houses  the  extra  air  often  finds  an 

outlet  through  crevices 

and  up  open  chimneys. 

,A    better    way    is    to 

provide  ventilation  by 

means  of  separate  flues. 

Since    the    heated   air 

rises  to  the  top  of  the 

room,  it   follows   that 

if    provision    is    made 

for  the  escape  of  the 

colder  air  by  flues  at 

the    floor,    the   incom- 
ing air  will  force  out 

the      foul      air,      thus          FIGURE  328.  — HEATING  BY  HOT  AIR. 


THE  RADIOMETER  315 

changing  the  air  of  the  room  and  warming  it  at  the  same 
time. 

Large  public  buildings  must  have  positive  means  of 
supplying  fresh  air  to  the  extent  of  about  50  cubic  feet 
per  minute  for  each  person.  For  this  purpose  large  fans 
driven  by  power  draw  in  fresh  air  from  the  outside  and 
force  it  through  flues  throughout  the  building.  The  air 
is  often  washed  or  filtered  on  its  way  in,  and  in  cold 
weather  is  heated  by  steam  pipes.  The  foul  air  is  forced 
out  through  openings  near  the  floor.  Sometimes  exhaust 
fans  draw  out  the  vitiated  air  through  the  ventilating 
ducts. 

371.  Radiation. — When  one  stands  near   a  hot  stove, 
one  is  warmed  neither  by  heat  conducted  nor  conveyed  by 
the  air.     The  heat  energy  of  a  hot  body  is  constantly 
passing  into  space  as  radiant  energy  in  the  ether  (§  243). 
Radiant  energy  becomes  heat  again  only  when  it  is  ab- 
sorbed by  bodies  upon  which  it  falls.     Energy  transmitted 
in  this  way  is,  for  convenience,  referred  to  as  radiant  heat, 
although  it  is  transmitted  as  radiant  energy,  and  is  trans- 
formed into  heat  only  by  absorption.     Radiant  heat  and 
light  are  physically  identical,  but  are  perceived  through 
different  avenues  of  sensation.     Radiations  that  produce 
sight  when  received  through  the  eye  give  a  sensation  of 
warmth  through  the   nerves   of   touch,  or   heat   a   ther- 
mometer when  incident  upon  it.     The  long  ether  waves 
do  not  affect  the  eye,  but  they  heat  a  body  which  absorbs 
them. 

372.  The  Radiometer.  —  Long  heat  waves   may  be  de- 
tected by  the  radiometer,  an  instrument  invented  by  Sir 
William  Crookes  in  1873  while  investigating  the  properties 
of  highly  attenuated  gases.     It  consists  of  a  glass  bulb 
from  which  the  air  has  been  exhausted  until  the  pressure 


316 


HEAT 


does  not  exceed  7mm.  of  mercury  (Fig.  329).  Within 
the  bulb  is  a  light  cross  of  aluminum  wire  carrying  small 
vanes  of  mica,  one  face  of  each  coated  with  lampblack. 
The  whole  is  mounted  to  rotate  on  a  vertical  pivot.  When 
the  instrument  is  placed  in  the  sun- 
light or  in  the  radiation  from  any 
heated  body,  the  cross  revolves  with 
the  blackened  faces  of  the  vanes 
moving  away  from  the  source  of 
heat. 

The  infrequent  collisions  among 
the  molecules  in  such  a  vacuum  pre- 
vent the  equalization  of  pressure 
throughout  the  bulb.  The  black- 
ened sides  of  the  vanes  absorb  more 
heat  than  the  bright  ones,  and  the 
gas  molecules  rebound  from  the 
warmer  surfaces  with  a  greater  ve- 
locity than  from  the  others,  thus 
giving  the  vanes  an  impulse  in  the 
opposite  direction.  This  impulse  is 
the  equivalent  of  a  pressure,  which  causes  the  vanes  to 
revolve. 

373.  Laws  of  Heat  Radiation  —  Place  a  radiometer  about  50  cm. 
from  a  small  lighted  lamp  and  note  the  effect  on  the  radiometer. 
Support  a  cardboard  screen  between  the  lamp  and  the  radiometer ; 
the  rotation  of  the  radiometer  at  once  becomes  slower. 

Hence,  Radiation  proceeds  in  straight  lines.  This  law 
is  illustrated  in  the  use  of  fire  screens  and  sunshades. 

Lay  a  meter  stick  on  a  table  and  place  the  radiometer  at  one  end 
of  it  and  the  lamp  at  the  other.  Count  the  number  of  revolutions  of 
the  vanes  in  one  minute.  Move  the  radiometer  to  a  distance  of  50  cm. 


FIGURE  329. — THE  RADI- 
OMETER. 


HEAT  TRANSPARENCY  317 

from  the  lamp  and  count  the  number  of  revolutions  again  for  a  minute. 
It  will  be  about  four  times  as  many  as  before. 

Hence,  The  amount  of  radiant  energy  received  by  a 
body  from  any  small  radiant  area  varies  inversely  as 
the  square  of  the  distance  from  it  as  a  source.  Note  that 
this  law  is  the  same  as  that  relating  to  the  intensity  of 
illumination  in  light  (§  252). 

Support  a  plane  mirror  vertically  on  a  table.  At  right  angles  to  it 
and  distant  about  5  cm.  support  a  vertical  cardboard  screen  about 
50cm.  long  and  20cm.  wide.  On  one  side  of  this  screen  place  a 
lighted  lamp  and  on  the  other  the  radiometer.  The  vanes  will  revolve 
rapidly  whenever  the  lamp  and  the  radiometer  are  in  such  a  position 
that  the  screen  bisects  the  angle  made  by  lines  drawn  from  them  to 
the  same  point  on  the  mirror.  The  angles  between  these  lines  and 
the  screen  are  the  angles  of  incidence  and  reflection  of  the  radiant 
energy. 

Hence,  Radiant  energy  is  reflected  from  a  polished  sur- 
face so  that  the  angles  of  incidence  and  reflection  are 
equal. 

Select  two  concave  wall  lamp  reflectors  of  the  same  size  and  blacken 
one  of  them  in  the  smoke  from  burning  camphor  gum.  Place  a 
lighted  lamp  about  one  meter  from  the  radiometer  and  observe  the 
rate  of  rotation  of  the  vanes.  Hold  the  clear  reflector  back  of  the 
radiometer,  so  as  to  concentrate  the  radiation  from  the  lamp  upon  it, 
and  again  note  the  rate  of  rotation.  Now  substitute  the  blackened 
reflector  for  the  clear  one;  the  rate  of  rotation  will  be  greatly  reduced. 

Hence,  The  capacity  of  a  surface  to  reflect  radiant 
energy  depends  both  on  the  polish  of  the  surface  and  on 
the  nature  of  the  material.  Polished  brass  is  one  of  the 
best  reflectors  and  lampblack  is  the  poorest. 

374.  Heat  Transparency.  —  Select  two  flat  twelve  ounce  bottles ; 
fill  one  with  water  and  the  other  with  a  solution  of  iodine  in  carbon 
disulphide.  Cut  an  opening  in  a  sheet  of  black  cardboard  of  such  a 


318  HEAT 

size  that  either  bottle  will  cover  it.  Place  this  cardboard  between  the 
lamp  and  the  radiometer  and  note  the  effect  on  the  radiometer  as  the 
opening  is  closed  successively  by  the  bottles.  This  experiment  and 
others  similar  to  it  show  that 

The  transmission  of  radiant  energy  through  various  sub- 
stances depends  on  the  temperature  of  the  source,  and  the 
thickness  and  nature  of  the  substance  itself. 

Substances  that  transmit  a  large  part  of  the  heat  energy, 
such  as  the  solution  of  iodine  and  rock  salt,  are  said  to  be 
diathermanous  ;  those  absorbing  a  large  part,  such  as  water, 
are  athermanous.  Glass  is  diathermanous  to  radiations 
from  a  source  of  high  temperature,  such  as  the  sun,  but 
athermanous  to  radiations  from  sources  of  low  tempera- 
ture, such  as  a  stove.  The  radiant  energy  from  the  sun 
passes  readily  through  the  atmosphere  to  the  earth,  and 
warms  its  surface ;  but  the  radiations  from  the  earth  are 
stopped  to  a  large  extent  by  the  surrounding  atmosphere. 
This  selective  absorption  is  due  in  large  measure  to  tho 
vapor  of  water  in  the  air. 

Questions 

1.  Why  will   newspapers   spread   over  plants  protect  them  from 
frost  ? 

2.  Why  does  a  tall  chimney  have  a  stronger  draft  than  a  short 
one? 

3.  Explain  how  it  is  possible  to  boil  water  in  a  paper  pail  with- 
out burning  the  pail. 

4.  Should  the  surface  of  a  steam  or  hot  water  radiator  be  rough 
or  polished  ? 

5.  In  what  way  does  a  stove  heat  a  room  ? 

6.  Why  does  a  woolen  garment  feel  warmer  than  a  cotton  or  a 
linen  one  ? 

7.  Why  is  glass  an  effective  screen  ? 


HEAT  FROM  MECHANICAL  ACTION  319 

8.  Why  does  steam  burn  more  severely  than  hot  water  ? 

9.  Why  should  the  registers  for  removing  impure  air  be  placed 
at  the  floor  level  ? 

10.  What  principles  of  heat  are  applied  in  the  radiator  of  an 
automobile  ? 

11.  Why  will  the  moistened  finger  or  the  tongue  freeze  quickly 
to  a  piece  of  very  cold  iron,  but  not  to  a  piece  of  wood? 

12.  Why  is  the  boiling  point  of  water  in  the  boiler  of  a  steam 
engine  above  100°C.? 

VII.  HEAT  AND  WORK 

375.  Heat  from  Mechanical  Action.  —  Strike  the  edge  of  a 
piece  of  flint  a  glancing  blow  with  a  piece  of  hardened  steel.  Sparks 
will  fly  at  each  blow. 

Pound  a  bar  of  lead  vigorously  with  a  hammer.  The 
temperature  of  the  bar  will  rise. 

In  the  cavity  at  the  end  of  a  piston  of  a  fire  syringe  place 
a  small  piece  of  tinder,  such  as  is  employed  in  cigar  lighters 
(Fig.  330).  Force  the  piston  quickly  into  the  barrel.  If 
the  piston  is  immediately  withdrawn  the  tinder  will  prob- 
ably be  on  fire. 

These  experiments  show  that  mechanical  en- 
ergy may  be  transformed  into  heat.  Some  of  the 
energy  of  the  descending  flint,  the  hammer,  and 
the  piston  has  in  each  case  been  transferred  to  the 
molecules  of  the  bodies  themselves,  increasing 
their  kinetic  energy,  that  is,  raising  their  tern- 

r  IGURE 
perature.  330.— 

Savages  kindle  fire  by  rapidly  twirling  a  dry  FlRE  SYR- 
stick,  one  end  of  which  rests  in  a  notch  cut  in  a 
second  dry  piece.  The  axles  of  carriages  and  the  bearings 
in  machinery  are  heated  to  a  high  temperature  when  not 
properly  lubricated.  The  heating  of  drills  and  bits  in 
boring,  the  heating  of  saws  in  cutting  timber,  the  burning 


320  HEAT 

of  the  hands  by  a  rope  slipping  rapidly  through  them,  the 
stream  of  sparks  flying  from  an  emery  wheel,  are  instances 
of  the  same  kind  of  transformation ;  the  work  done  against 
friction  produces  kinetic  energy  in  the  form  of  heat. 

376.  The  Mechanical  Equivalent  of  Heat.  —  In  1840  Joule 
of  Manchester  in  England  began  a  series  of  experiments 
to  determine  the  numerical  relation  between  the  unit  of 
heat   and   the   foot   pound.      His   experiments   extended 
over  a  period  of  forty  years.     His  most  successful  method 
consisted  in  measuring  the  heat  produced  when  a  meas- 
ured amount  of  work  was  expended  in  heating  water  by 
stirring  it  with  paddles  driven  by  weights  falling  through 
a  known  height.     His  final  result  was    that    772   ft.-lb, 
of  work,  when  converted  into  heat,  raise  the  temperature 
of  1  Ib.  of  water  1°  F.,  or  1390  ft.-lb.  for  1°  C.     The  later 
and  more  elaborate  researches  of  Rowland  in  1879  and  of 
Griffiths  in  1893  show  that  the  relation  is  778  ft.-lb.  for 
1°F.,  or  427.5  kg.-m.  for  1°  C.  ;  that  is,  if  the  work  done 
in  lifting  427.5  kg.  one  meter  high  is  all  converted  into 
heat,  it  will  raise  the  temperature  of  1  kg.  of  water  1°  C. 
This  relation  is  known  as  the  mechanical  equivalent  of  heat. 
Its  value  expressed  in  absolute  units  is  4.19  x  107  ergs 
per  calorie. 

377.  The  Steam  Engine. — The  most  important  devices 
for  the  conversion  of  heat  into  mechanical  work  are  the 
steam  engine  and  the   gas   engine.     The   former   in   its 
assential  features  was  invented  by  James  Watt.     In  the 
reciprocating  steam  engine  a  piston  is  moved  alternately 
in  opposite  directions  by  the  pressure  of  steam  applied 
first  to  one  of  its  faces  and  then  to  the  other.     This  re- 
ciprocating or  to-and-fro  motion  is  converted  into  rotatory 
motion  by  the  device  of  a  connecting  rod,  a  crank,  and  a 
flywheel. 


James  Watt  (1736-1819)  was  born  at  Greenock,  Scotland,  and 
was  educated  as  an  instrument  maker.     In  studying  the  defects  of 

the  steam  engines  then  in  use, 
he  was  led  to  make  many 
very  important  improvements, 
culminating  in  his  invention 
of  the  double-acting  steam 
engine.  He  invented  the  ball 
governor,  the  cylinder  jacket, 
the  D-valve,  the  jointed  paral- 
lelogram for  securing  recti- 
linear motion  to  the  piston, 
the  mercury  steam-gauge, 
and  the  water-gauge.  He  is 
also  to  be  credited  with  the  first 
compound  engine,  a  type  of  en- 
gine extensively  used  to-day. 


James  Prescott  Joule  (1818-1889),  the  son  of  a  Manchester 
brewer,  was  born  at  Salford, 
England.  He  became  known 
to  the  scientific  world  through 
his  contributions  in  heat,  elec- 
tricity, and  magnetism.  His 
greatest  achievement  was  es- 
tablishing the  modern  kinetic 
theory  of  heat  by  determining 
the  mechanical  equivalent  of 
heat.  His  experiments  on  this 
subject  were  continued 
through  a  period  of  forty  years. 
In  recognition  of  his  great  work 
he  was  presented  with  the 
Royal  Medal  of  the  Royal  So- 
ciety of  England  in  1852. 


THE  STEAM  ENGINE 


321 


R 


In  Fig.  331  are  shown  in  section  the  cylinder,  piston, 
and  valve  of  a  slide-valve  steam  engine.  The  piston  B  is 
moved  in  the  cylinder  A  by  the  pressure  of  the  steam  ad- 
mitted through  the  inlet  pipe  a.  The  slide  valve  d  works 
in  the  steam  chest  cc 
and  admits  steam  al- 
ternately to  the  two 
ends  of  the  cylinder 
through  the  steam 
ports  at  either  end. 

When  the  valve  is 
in  the  position  shown, 
steam  passes  into  the 
right-hand  end  of  the 
cylinder  and  drives 
the  piston  toward  the 

left.     At     the     same 

FIGURE  331.  —  CYLINDER  OF  STEAM  ENGINE. 
time  the  other  end  is 

connected  with  the  exhaust  pipe  ee  through  which  the 
steam  escapes,  either  into  the  air,  as  in  a  high-pressure 
non- condensing  engine,  or  into  a  large  condensing  chamber, 
as  in  a  low  pressure  condensing  engine. 

The  slide  valve  d  is  moved  by  the  rod  R,  connected  to 
an  eccentric,  which  is  a  round  disk  mounted  a  little  to  one 
side  of  its  center,  on  the  engine  shaft.  It  has  the  effect 
of  a  crank.  The  flywheel,  also  mounted  on  the  shaft  of 
the  engine,  has  a  heavy  rim  and  serves  as  a  store  of  energy 
to  carry  the  shaft  over  the  dead  points  when  the  piston  is 
at  either  end  of  the  cylinder.  There  is  in  the  flywheel  a 
give-and-take  of  energy  twice  every  revolution,  and  a 
fairly  steady  rotation  of  the  shaft  is  the  result. 

The  eccentric  is  set  in  such  a  way  that  the  rod  R  closes 
the  valve  admitting  steam  to  either  end  of  the  cylinder 


322  HEAT 

before  the  piston  has  completed  its  stroke ;  the  motion  of 
the  piston  is  continued  during  the  remainder  of  the  stroke 
by  the  expansive  force  of  the  steam. 

Corliss  valves  are  commonly  used  in  large  slow  speed 
engines.  As  distinguished  from  the  slide  valve,  the 
Corliss  valve  is  cylindrical  and  opens  and  closes  by  turn- 
ing a  little  in  its  seat,  first  in  one  direction  and  then  the 
other.  In  the  Corliss  engine  there  are  four  such  valves,  two 
at  each  end  of  the  steam  cylinder.  One  of  each  pair  admits 
steam  to  the  cylinder  and  the  other  is  the  exhaust  valve. 
When  the  inlet  valve  is  open  at  one  end  of  the  steam  cylin- 
der, the  exhaust  valve  is  open  at  the  other  end.  All  four 
valves  are  opened  and  closed  automatically  by  the  motion  of 
the  engine  itself.  Each  valve  can  be  adjusted  separately. 

378.  The  Indicator  Diagram.  —  The  steam  indicator  is  a  device 
for  the  automatic  tracing  of  a  diagram  representing  the  relation  be- 
tween the  volume  and  the  pressure  of  the  steam 
in  the  cylinder  during  one  stroke.     This  dia- 
gram is  known  as  an  "indicator  card  "  (Fig. 

332). 

From  a  to  b  the  inlet  port 
is  open  and  the  full  pressure 

Volume  of  steam  is  on  the  piston ;  at 

FIGURE  332.  —  INDICATOR  DIAGRAM.  &  the  inlet  port  closes  and 

the  steam  expands  from  b  to 

c,  when  the  exhaust  port  opens ;  at  d  the  pressure  is  reduced  to 
the  lowest  value  and  remains  sensibly  constant  during  the  return 
movement  of  the  piston  until  e  is  reached,  when  the  exhaust  port 
closes  and  the  remaining  steam  is  compressed  from  e  to/  At  /  the 
inlet  port  opens  and  the  pressure  rises  abruptly  to  the  initial  maxi- 
mum, thus  completing  the  cycle.  The  work  done  during  the  stroke 
is  represented  by  the  inclosed  area  abcdef.  The  indicator  card  is  used 
also  in  adjusting  the  valves. 

379.  The  Steam  Turbine. — The  steam  turbine   has   the 
great  advantage  of  producing  rotary  motion  directly  with- 


ABOVE  :   SECTION  THROUGH  THE  STEAM  TURBINE,  SHOWING  NOZZLES  AND  BUCKETS. 

BELOW  :  THE  ROTOR  OF  A  TURBINE,  SHOWING  BUCKETS  INCREASING  IN  SIZE 

FROM  LEFT  TO  RIGHT. 


THE  GAS  ENGINE  323 

out  the  intervention  of  a  connecting  rod  and  crank  to 
convert  the  back  and  forth  motion  of  the  piston  in  a 
reciprocating  engine  into  rotary  motion.  In  the  latter 
the  piston  stops  and  starts  again  twice  during  each  revo- 
lution of  the  flywheel,  and  the  stopping  and  starting  gives 
rise  to  disagreeable  vibrations.  In  the  steam  turbine  the 
rotor  revolves  continuously  and  the  impulses  it  receives 
are  constant  instead  of  intermittent. 

Steam  enters  the  turbine  through  a  set  of  stationary 
nozzles,  shown  in  section  in  the  half  tone.  Here  it  expands 
and  acquires  a  high  velocity.  It  then  strikes  the  entrance 
edge  of  the  first  row  of  buckets  in  the  rotor,  gives  up  en- 
ergy to  them,  and  drives  them  forward  as  it  passes 
through.  It  then  passes  through  the  second  set  of  sta- 
tionary nozzles,  of  greater  area  than  the  first ;  here  it 
again  expands,  increases  its  velocity,  and  enters  the  second 
row  of  buckets.  The  process  is  repeated  in  successive 
stages  until  it  reaches  the  exhaust  outlet.  By  its  im- 
pulse on  each  row  of  buckets  it  gives  up  energy  to  the 
rotor.  The  half  tone  of  a  complete  rotor  shows  the  in- 
creasing size  of  the  buckets  from  left  to  right.  The 
buckets  are  curved  openings  through  the  rotor,  as  shown 
in  section  in  the  half  tone. 

380.  The  Gas  Engine.  —  The  gas  engine  is  a  type  of  in- 
ternal combustion  engine,  which  includes  motors  using  gas, 
gasoline,  kerosene,  or  alcohol  as  fuel.  The  fuel  is  intro- 
duced into  the  cylinder  of  the  engine,  either  as  a  gas  or  as 
a  vapor,  mixed  with  the  proper  quantity  of  air  to  produce  a 
good  explosive  mixture.  The  mixture  is  ignited  at  the 
right  instant  by  means  of  an  electric  spark.  The  explo- 
sion and  the  expansive  force  of  the  hot  gases  drive  the 
piston  forward  in  the  cylinder. 

In  the  four-cycle  type  of  gas  engine,  the  explosive  mix- 


324 


HEAT 


ture  is  drawn  in  and  ignited  in  each  cylinder  only  every 
other  revolution  of  the  engine,  while  in  the  two-cycle  type 
an  explosion  occurs  every  revolution.  The  former  type 
is  used  in  most  motor  car  engines,  and  the  latter  in  small 
motor  boats. 

The  operation  of  a  four-cycle  engine  is  illustrated  in  1, 
2,  3,  and  4  of  Fig.   333,  which  shows  the  four  steps  in  a 

complete  cycle.  The  inlet  valve 
a  and  the  exhaust  valve  b  are 
operated  by  the  cams  c  and  d. 
Both  valves  are  kept  normally 
closed  by  springs  surrounding  the 
valve  stems.  The  small  shafts  to 
which  the  two  cams  are  fixed  are 
driven  by  the  spur  wheel  e  on 
the  shaft  of  the  engine.  This 
wheel  engages  with  the  two  larger 
spur  wheels  on  the  cam  shafts, 
each  having  twice  as  many  teeth 
as  e  and  forming  with  it  a  two- 
to-one  gear,  so  that  c  and  d  rotate 
once  in  every  two  revolutions  of 
the  crank  shaft.  The  piston  m 
has  packing  rings ;  h  is  the  con- 
necting rod,  k  the  crank  shaft,  and  I  the  spark  plug. 
In  diagram  1  the  piston  is  descending  and  draws  in  the 
charge  through  the  open  valve  a ;  in  2  both  valves  are 
closed  and  the  piston  compresses  the  explosive  charge  5 
about  the  time  the  piston  reaches  its  highest  point,  the 
charge  is  ignited  by  a  spark  at  the  spark  plug,  and  the 
working  stroke  then  takes  place,  as  in  3,  both  valves 
remaining  closed  ;  in  4  the  exhaust  valve  b  is  opened  by 
the  cam  d,  and  the  products  of  the  combustion  escape 


FIGURE  333.  —  SHOWING  FOUR 
STEPS  IN  CYCLE. 


FRONT  AND  REAR  VIEWS  OF  AN  AERIAL  "FLIVVER. 
One  of  the  smallest  practical  airplanes  made. 


THE  AIRPLANE 


325 


through  the  muffler,  or  directly  into  the  open  air.  The 
piston  has  now  traversed  the  cylinder  four  times,  twice  in 
in  each  direction,  and  the  series  of  operations  begins  again. 

381.  Two-Cycle  Engine.  —  Figure  334  is  a  section   of  a 
two-cycle  gas  engine.     During  the  up-stroke  of  the  piston 
P  a  charge  is  drawn  through  A  into  the  crank  case  0. 
At  the  same  time  a  charge  in  the  cylinder  is  compressed 
and  is  ignited  by  a  spark  when  the 

compression  is  greatest.  The  piston 
is  forced  down,  and  when  it  passes 
the  port  E  the  exhaust  takes  place. 
When  the  admit  port  /  is  passed, 
a  charge  enters  from  the  crank 
case.  To  prevent  this  charge  from 
passing  across  and  escaping  at  E,  it 
is  made  to  strike  against  a  projec- 
tion J2  on  the  piston,  which  deflects 
it  upward.  The  momentum  of  the 
balance  wheel  carries  the  piston  up- 
ward, compresses  the  charge,  and 
,  j.  i  i_  •  ,  j.iT  i  FIGURE  334.  — SECTION  OP 

draws  a  fresh  charge  into  the  crank         TWO-CYCLE  ENGINE 

case.     The  piston  has  now  traversed 

the  cylinder  twice,  once  in  each  direction,  and  the  same 

series  of  operations  is  again  repeated. 

For  a  more  complete  discussion  of  gas  engines  and  auto- 
mobiles, see  Chapter  XV,  page  460. 

382.  The  Airplane.  —  The  principle  of  the  airplane  has 
already  been  described  in  §  124.     It  is  a  "  heavier  than 
air  "  machine  and  is  lifted  as  the  kite  is  lifted  ;  but  instead 
of  the  wind  blowing  against  it,  it  is  forced  against  the  air 
by  a  powerful  gas  engine,  driving  a  high  speed  propeller. 
Formerly  the  engine  and  the  propeller  were  at  the  rear 
end,  but  recent  practice  is  to  mount  them  in  front. 


326  HEAT 

Questions  and  Problems 

1.  Why  does  the  temperature  of  the  air  under  the  bell  jar  of  an 
air  pump  fall  when  the  pump  is  worked  ? 

2.  Is  there  a  difference  in  the  temperature  of  the  steam  as  it  enters 
a  steam  engine  and  as  it  leaves  at  the  exhaust  ?     Explain. 

3.  Lead  bullets  are  sometimes  melted  when  they  strike  a  target. 
Explain. 

4.  Does  clothing  keep  the  cold  out  or  keep  the  heat  in  ? 

5.  Is  there  any  less  moisture  in  the  air  after  it  has  passed  through 
a  heated  furnace  into  a  room  than  there  was  before  ? 

6.  Why  does  the  rapid  driving  of  an  automobile  heat  the  air  in 
the  tires? 

7.  A  mass  of  200  g.  moving  with  a  speed  of  50  m.  per  second  is 
suddenly  stopped.     If  all  its  energy  is  converted  into  heat,  how  many 
calories  would  be  generated  ? 

NOTE.     A  calorie  equals  4.19  x  107  ergs. 

8.  If  all  the  potential  energy  of  a  300  kg.  mass  of  rock  is  con- 
verted into  heat  by  falling  vertically  200  m.,  how  many  calories  would 
be  generated  ? 

9.  How  high  could  a  200  g.  weight  be  lifted  by  the  heat  required 
to  melt  the  same  mass  of  ice,  if  all  the  heat  could  be  utilized  for  the 
purpose  ? 

10.  If  the  average  pressure  of  steam  in  the  cylinder  of  an  engine  is 
100  Ib.  per  square  inch,  the  area  of  the  piston  is  80  sq.  in.,  and  the 
stroke  1  ft.,  how  many  horse  powers  would  be  developed  if  the 
engine  makes  two  revolutions  per  second  ? 


CHAPTER  X 


MAGNETISM 
I.  MAGNETS  AND   MAGNETIC  ACTION 

383.  Natural  Magnets  or  Lodestones.  —  Black  oxide  of 
iron,  known  to  mineralogists  as  magnetite,  is  found  in  many 
parts  of  the  world,  notably  in  Arkansas,  the  Isle  of  Elba, 
Spain,  and  Sweden.  Some  of  these  hard  black  stones  are 
found  to  possess  the  property  of  attracting  to  them  small 
pieces  of  iron.  At  a  very  early  date  such  pieces  of  iron 
ore  were  found  near  Magnesia  in  Asia  Minor,  and  they 
were  therefore  called  magnetic  stones  and  later  magnets. 
They  are  now  known  as  natural  magnets,  and  the  properties 
peculiar  to  them  as  magnetic  properties. 

Dip  a  piece  of  natural  magnet  into  iron  filings  ;  they  will  adhere 

to  it  in  tufts,  not  uniformly  over  its  surface,  but  chiefly  at  the  ends 

and  on  projecting  edges  (Fig.  335). 

Suspend  a  piece  of  natural  magnet  by  a 

piece  of  untwisted  thread  (Fig.  336),  or  float 

it  on  a  wooden  raft  on  water.  Note  its  posi- 
tion, then  disturb  it 
slightly,  and  again  let  it 

come  to  rest.  It  will  be  found  that  it  invariably 
returns  to  the  same  position,  the  line  connecting 
the  two  ends  to  which  the  filings  chiefly  adhered 
in  the  preceding  experiment  lying  north  and 
south. 


FIGURE  335.  —  NATURAL 
MAGNET. 


FENDED. 


This  directional  property  of  the  natu- 
ral  magnet  was  early  turned  to  account 


327 


328  MAGNETISM 

in  navigation,  and  secured  for  it  the  name  of  lodestone 
(leading-stone). 

384.  Artificial  Magnets.  —  Stroke  the  blade  of  a  pocket  knife 
from  end  to  end,  and  always  in  the  same  direction,  with  one  end  of  a 
lodestone.     Touch  it  to  iron  filings ;  they  will  cling  to  its  point  as 
they  did  to  the  lodestone.     The  knife  blade  has  become  a  magnet. 

Use  the  knife  blade  of  the  last  experiment  to  stroke  another  blade. 
This  second  blade  will  also  acquire  magnetic  properties,  and  the  first 
one  has  suffered  no  loss. 

Artificial  magnets,  or  simply  magnets,  are  bars  of  hard- 
ened steel  that  have  been  made  magnetic  by  the  applica- 
tion of  some  other  magnet  or  magnetizing  force.  The 
form  of  artificial  magnets  most  commonly  met  with  are 
the  bar  and  the  horseshoe. 

385.  Magnetic  Substances.  —  Any  substance  that  is  at- 
tracted by  a  magnet  or  that  can  be  magnetized  is  a  mag- 
netic  substance.     Faraday  showed   that   most   substances 
are  influenced  by  magnetism,  but  not  all  in  the  same  way 
nor  to  the  same  degree.     Iron,   nickel,   and    cobalt   are 
strongly  attracted  by  magnets  and  are  said  to  be  mag- 
netic; bismuth,  antimony,  phosphorus,  and  copper  act  as 
if  they  are  repelled  by  magnets  and  they  are  called  dia- 

magnetic.     Most  of  the  alloys 
of    iron    are    magnetic,    but 
.-  MAGNET  TOT™H    manganese  steel  is  non-mag- 

IRON  FILINGS.  netic. 

386.  Polarity.  —  Roll  a  bar  magnet  in  iron  filings.     It  will  be 
come  thickly  covered  with  the  filings  near  its  end.     Few,  if  any,  will 
adhere  at  the  middle  (Fig.  337) . 

The  experiment  shows  that  the  greater  part  of  the  mag- 
netic attraction  is  concentrated  at  or  near  the  ends  of  the 
magnet.  They  are  called  its  poles,  and  the  magnet  is  said 


MAGNETIC  TRANSPARENCY  329 

to  have  polarity.  The  line  joining  the  poles  of  a  long 
slender  magnet  is  its  magnetic  axis. 

387.  North  and  South  Poles.  —  Straighten  a  piece  of  watch 
spring  8  or  10  cm.  long,  stroke  it  from  end  to  end  with  a  magnet,  and 
float  it  on  a  cork  in  a 
vessel  of  water  (Fig. 
338).  It  will  turn  from 
any  other  position  to  a 
north  and  south  one, 
and  invariably  with  the 
same  end  north.  FIGURE  338.  —  FLOATING  MAGNET. 

The  end  of  a  magnet 

pointing  toward  the  north  is  called  the  north-seeking  pole,  and  the  other, 
the  south-seeking  pule.  They  are  commonly  called  simply  the  north  pole 
and  the  south  pole. 

388.  Magnetic  Needle.  —  A  slender  magnetized  bar,  sus- 
pended by  an  untwisted  fiber  or  pivoted  on  a  point  so  as 
to  have  freedom  of  motion  about  a  vertical  axis  is  a  mag- 
netic needle  (Fig.  339).  The 
direction  in  which  it  comes  to 
rest  without  torsion  or  friction 
is  called  the  magnetic  meridian. 


Fasten  a  fiber  of  unspun^  silk  to 
a  piece  of  magnetized  watch  spring 
about  2  cm.  long  so  that  it  will  hang 
horizontally.  Suspend  it  inside  a 
wide-mouthed  bottle  by  attaching 
the  fiber  to  a  cork  fitting  the  mouth 

FIGURE  339. -MAGNETJC  NEEDLE.      of   the  bottle'     The  little  magnetic 

needle  will  then  be  protected  from 

currents  of  air.     It  may  be  made  visible  at  a  distance  by  sticking  fast 
to  it  a  piece  of  thin  white  paper. 

389.  Magnetic  Transparency.  —  Cover  the  pole  of  a  strong  bar 
magnet  with  a  thin  plate  of  glass.  Bring  the  face  of  the  plate  oppo- 
site the  pole  in  contact  with  a  pile  of  iron  tacks.  A  number  will  be 


330  MAGNETISM 

found  to  adhere,  showing  that  the  attraction  takes  place  through 
glass.  In  like  manner,  try  thin  plates  of  mica,  wood,  paper,  zinc, 
copper,  and  iron.  No  perceptible  difference  will  be  seen  except  in 
the  case  of  the  iron,  where  the  number  of  tacks  lifted  will  be  much 


Magnetic  force  acts  freely  through  all  substances  except 
those  classified  as  magnetic.  Soft  iron  serves  as  a  more  or 
less  perfect  screen  to  magnetism.  Watches  may  be  pro- 
tected from  magnetic  force  that  is  not  too  strong  by  means 
of  an  inside  case  of  soft  sheet  iron. 

390.  First  Law  of  Magnetic  Action.  —  Magnetize  a  piece  of 
large  knitting  needle,  about  four  inches  long,  by  stroking  it  from  the 
middle  to  one  end  with  the  north  pole  of  a  bar  magnet,  and  then 
from  the  middle  to  the  other  end  with  the  south  pole.     Repeat  the 
operation  several  times.     Present  the  north  pole  of  the  magnetized 
knitting  needle  to   the   north   pole  of   the  needle  suspended  in  the 
bottle.     The  latter  will  be  repelled.     Present  the  same  pole  to  the 
south  pole  of  the  little  magnetic  needle ;  it  will  be  attracted.     Repeat 
with  the  south  pole  of  the  knitting  needle  and  note  the  deflections. 

The  results  may  be  expressed  by  the  following  law  of 
magnetic  attraction  and  repulsion  : 

Like  magnetic  poles  repel  and  unlike  magnetic  poles 
attract  each  other. 

391.  Testing  for  Polarity.  —  The  magnetic  needle  affords 
a  ready  means  of  ascertaining  which  pole  of  a  magnet  is 
the  north  pole,  for  the  north  pole  of  the  magnet  is  the  one 
that  repels  the  north  pole  of  the  magnetic  needle.     Repul- 
sion is  the  only  sure  test  of  polarity  for  reasons  that  will 
appear  in  the  experiments  that  follow. 

392.  Induced  Magnetism.  —  Hold  vertically  a  strong  bar  magnet 
and  bring  up  against  its  lower  end  a  short  cylinder  of  soft  iron.     It 
will  adhere.     To  the  lower  end  of  this  one  attach  another,  and  so  on 


UNLIKE  POLARITY  INDUCED  331 

in  a  series  of  as  many  as  will  stick  (Fig.  340).  Carefully  detach  the 
magnet  from  the  first  piece  of  iron  and  withdraw  it  slowly.  The 
pieces  of  iron  will  all  fall  apart. 

The  small  bars  of  iron  hold  together 
because  they  become  temporary  mag- 
nets. Magnetism  produced  in  mag- 
netic substances  by  the  influence  of  a 
magnet  near  by  or  in  contact  with 
them  is  said  to  be  induced,  and  the 
action  is  called  magnetic  induction. 

Magnetic    induction   precedes   attrac- 
.    '  FIGURE  340.  —  INDUCED 

MAGNETISM. 


393.  Unlike  Polarity  Induced.  —  Place  a  bar  magnet  in  line 
with  the  magnetic  axis  of  a  magnetic  needle,  with  its  north  pole  as 
near  as  possible  to  the  north  pole  of  the  needle  without  appreciably 
repelling  it  (Fig.  341).  Insert  a  bar  of  soft  iron  between  the  magnet 

and  the  needle.  The  north  pole 
of  the  needle  will  be  immedi- 
ately repelled. 


The    repulsion    of    the 

north  pole  of  the  needle  by 
FIGURE  341 .  -  POLARITY  BY  INDUCTION.     the  end  of  the  soft  ipon  bar 

next  to  it  shows  that  this  end  of  the  bar  has  acquired 
a  polarity  the  same  as  that  of  the  magnet,  that  is,  north 
polarity.  Then  the  other  end  adjacent  to  the  magnet 
must  have  acquired  the  opposite  polarity. 

When  a  magnet  is  brought  near  a  piece  of  iron,  the  iron 
is  magnetized  by  induction,  and  there  is  attraction  because 
the  adjacent  poles  are  unlike.  When  a  bunch  of  iron  fil- 
ings or  tacks  adhere  to  a  magnet,  each  filing  or  tack  be- 
comes a  magnet  and  acts  inductively  on  the  others  and  all 
become  magnets.  Weak  magnets  may  have  their  polarity 
reversed  by  the  inductive  action  of  a  strong  magnet. 


332  MAGNETISM 

394.  Permanent   and    Temporary  Magnetism.  —  When  a 
piece  of   hardened  steel   is   brought   near   a   magnet,   it 
acquires  magnetism  as  a  piece  of   soft  iron    does   under 
the  same  conditions :  but  the  steel  retains  its  magnetism 
when  the  magnetizing  force  is  withdrawn,  while  the  soft 
iron  does  not.     In  the  experiment  of  §  392  the  soft  iron 
ceases  to  be  a  magnet  when  removed  to  a  distance  from 
the  bar  magnet.     In  addition,  therefore,  to  the  permanent 
magnetism   exhibited   by  the  magnetized  steel,  we   have 
temporary  magnetism  induced  in  a  bar  of  soft  iron  when  it 
is  brought  near  a  magnet  or  in  contact  with  it. 

II.  NATURE  OF  MAGNETISM 

395.  Magnetism  a  Molecular  Phenomenon.  —  If  a  piece  of 
watch  spring  be  magnetized  and  then  heated  red  hot,  it  will  lose  its 
magnetism  completely. 

A  magnetized  knitting  needle  will  not  pick  up  as  many  tacks  after 
being  vibrated  against  the  edge  of  a  table  as  it  did  before. 

A  piece  of  moderately  heavy  and  very 
soft  iron  wire  of  the  form  shown  in 

Fig.  342  can  be  magnetized  by  stroking 
FIGURE  342.  —  BENT  MAGNET.          *  J  T,     . 

it  gently  with  a  bar  magnet.     If  given 

a  sudden  twist,  it  loses  at  once  all  the  magnetism  imparted  to  it. 

A  piece  of  watch  spring  attracts  iron  filings  only  at  its  ends.  If 
broken  in  two  in  the  middle,  each  half  will  be  a  magnet  and  will 
attract  filings,  two  new  poles  having  been  formed  where  the  original 
magnet  was  neutral.  If  these  pieces  in  turn  be  broken,  their  parts 
will  be  magnets.  If  this  division  into  separate  magnets  be  conceived 
to  be  carried  as  far  as  the  molecules,  they  too  would  probably  be 
magnets. 

It  is  worthy  of  notice  that  magnetization  is  facilitated 
by  jarring  the  steel,  or  by  heating  it  and  letting  it  cool 
under  the  influence  of  a  magnetizing  force.  If  an  iron 
bar  is  rapidly  magnetized  and  demagnetized,  its  tempera- 
ture is  raised.  A  steel  rod  is  slightly  lengthened  by 


MAGNETIC  FIELDS  333 


magnetization  and  a  faint  click  may  be  heard  if 
the  magnetization  is  sudden. 

396.  Theory  of  Magnetism.  —  The  facts  of  the 
preceding  section  indicate  that  the  seat  of  mag- 
netism is  the  molecule,  that  the  individual  mole- 
cules are  magnets,  that  in  an  unmagnetized 
piece  of  iron  the  poles  of  the  molecular  magnets 
are  turned  in  various  directions,  so  that  they 
form  stable  combinations  or  closed  magnetic 
chains,  and  hence  exhibit  no  magnetism  external 
to  the  bar  (Fig.  343).  In  a  magnetized  bar  the  FIGURE 
larger  portion  of  the  molecules  have 


eeee 
eeee 
eiii 
iiee 
.... 
ey  BB 

iiiB 
BBBB 
.... 
.... 

BBBB 
BBBB 
BBBB 


their  magnetic  axes  pointing  in  the  same     NETIZED 
direction   (Fig.  344),  the  completeness     BAR- 
of  the  magnetization  depending  on  the  complete- 
ness of  this  alignment. 

III.   THE  MAGNETIC  FIELD 

397.  Lines  of  Magnetic  Force.  —  Place  a  sheet  of 
paper  over  a  small  bar  magnet  and  sift  iron  filings  evenly 
over  it  from  a  bottle  with  a  piece  of  gauze  tied  over  the 
mouth,  tapping  the  paper  gently  to  aid  the  filings  in  ar- 
FIGURE      ranging  themselves  under  the  influence  of  the   magnet. 
344.—       They  will  cling  together  in  curved  lines,  which  diverge 
MAGNET-      frOm  one  pole  of  the  magnet  and  meet  again  at  the  oppo- 
IZEDBAR.      site  pole 

These  lines  are  called  lines  of  magnetic  force  or  of  mag- 
netic induction.  Each  particle  of  iron  becomes  a  magnet 
by  induction  ;  hence  the  lines  of  force  are  the  lines  along 
which  magnetic  induction  takes  place. 

398.  Magnetic  Fields.  —  A  magnetic  field  is  the  space 
around  a  magnet  in  which  there  are  lines  of  magnetic 
force. 


334 


MAGNETISM 


Figure  345  was  made  from  a  photograph  of  the  magnetic  field  of  a 
bar  magnet  in  a  plane  passing  through  the  magnetic  axis.  These 
lines  branch  out  nearly  radially  from  one  pole  and  curve  round 
through  the  air  to  the  other  pole.  Faraday  gave  to  them  the  narne 


FIGURE  345.  —  MAGNETIC  FIELD  OF  BAR  MAGNEI. 


lines  of  force.     The  curves  made  by  the  iron  filings  "represent  visibly 

the  invisible  lines  of  magnetic  force." 

Figure  34G  shows  the  field  about  two  bar  magnets  placed  with  their 

unlike  poles  adjacent  to  each  other.     Many  of  the  lines  from  the  north 

pole  of  the  one  extend  across  to  the  south  pole  of  the  other,  and  this 
connection     denotes     at- 
traction. 

Figure  317  shows  the 
field  about  two  bar  mag- 
nets with  their  like  poles 
adjacent  to  each  other. 
None  of  the  lines  spring- 
ing from  either  pole  ex- 
tend across  to  the  neigh- 
boring pole  of  the  other 
magnet.  This  is  a  pic- 


FIGURE  346.  —  MAGNETIC  FIELD,  Two  UNLIKE 
POLES. 


ture   of    magnetic   repul- 
sion. 


399.  Properties  of  Lines  of  Force.  —  Lines  of  magnetic 
force  have  the  following  properties :  (a)  They  are  under 
tension,  exerting  a  pull  in  the  direction  of  their  length ; 


PERMEABILITY 


335 


(£>)  they  spread  out  as  if  repelled  from  one  another  at 
right  angles  to  their  length ;  (<?)  they  never  cross  one 
another. 

400.  Direction  of 
Lines  of  Force.  — 
Hold  a  mounted  magnetic 
needle  about  1  cm.  long 
near  a  bar  magnet.  It 
will  place  itself  tangent 
to  the  line  of  force  passing 
through  it. 

Suspend  by  a  fine 
thread  about  60  cm.  long 
a  strongly  magnetized 


FIGURE  347.  —  MAGNETIC  FIELD,  Two  LIKE 
POLES. 


sewing  needle  with  its  north  pole  downward.  Bring  this  pole  of  the 
needle  over  the  north  pole  of  a  horizontal  bar  magnet  (Fig.  348).  It 
will  be  repelled  and  will  move  along  a  curved  line  of  force  toward  the 
south  pole  of  the  magnet. 

The  direction  of  a  line  of  force  at  any  point  is  that  of 
a  line  drawn  tangent  to  the  curve  at  that  point,  and  the 

positive  direction  is 
that  in  which  a  north 
pole  is  urged.  Since 

m~~  ~~7 —         ~~ 7      the  north  pole  of   a 

/      magnetic  needle  is  re- 
^tfS!™*              ^p       I       pelled  by   the   north 
I        pole  of  a  bar  magnet, 
/         an  observer  standing 
J          with  his  back  to  the 

north  pole  of  a  mag- 

FIGURE  348.  —  DIRECTION  OF  LINES  OF  FORCE.  *.       .  . ° 

net  looks  in  the  di- 
rection of  the  lines  of  force  coming  from  that  pole. 

401.  Permeability.  —  Place  a  piece  of  soft  iron  near  the  pole  of 
a  bar  magnet  and  map  out  the  field  with  iron  filings.  The  lines  are 
displaced  by  the  iron  and  are  gathered  into  it  (Fig.  349). 


336 


MAGNETISM 


When  iron  is  placed  in  a  magnetic  field,  the  lines  of 
force  are  concentrated  by  it.     This  property  possessed  by 

iron,  when  placed 
in  a  magnetic 
field,  of  concen- 
trating the  lines 
of  force  and  in- 
creasing their 
number,  is  known 
as  permeability. 
The  superior  per- 
meability of  soft 
iron  explains  the 
action  of  magnetic  screens  (§  389).  In  the  case  of  the 
watch  shield,  the  lines  of  force  follow  the  iron  and  do  not 
cross  it ;  the  watch  is  thus  protected  from  magnetism  be- 
cause the  lines  of  force  do  not  pass  through  it  except  when 
the  magnetic  field  is  very  strong. 


FIGURE  349.  —  DISPLACEMENT  OF  LINES. 


IV.   TERRESTRIAL  MAGNETISM 

402.  The  Earth  a  Magnet.  —  Support  a  thoroughly  annealed 
iron  rod  or  pipe  horizontally  in  an  east-and-west  line  and  test  it  for 
polarity.  It  should  show  no  magnet- 
ism. Now  place  it  north  and  south 
with  the  north  end  about  70°  below 
the  horizontal  (Fig.  350).  While  in 
this  position,  tap  it  with  a  hammer 
and  then  test  it  for  polarity.  The 
lower  end  will  be  found  to  be  a  north 
pole  and  the  upper  end  a  south  pole. 
Turn  the  rod  end  for  end,  hold  in  the 
former  position,  and  tap  again  with  a 
hammer.  The  lower  end  will  again 
become  a  north  pole  ;  the  magnetism  FIGURE  350.—  EARTH  INDUCED 
has  been  reversed.  MAGNETISM. 


MAGNETIC  DIP 


337 


This  experiment  shows  that  the  earth  acts  as  a  magnet 
on  the  iron  rod  and  magnetizes  it  by  induction.  Similarly, 
iron  objects,  such  as  a  stove,  a  radiator,  vertical  steam 
pipes,  iron  columns,  and  hitching 
posts,  become  magnets  with  the 
lower  end  a  north  pole.  The  in- 
ductive action  of  the  earth  as  a 
magnet  accounts  for  the  magnet- 
ism of  natural  magnets. 

>IAO     -M-          A-      TV  FIGURE  351.  —  MAGNETIC  DIP. 

403.   Magnetic    Dip.  —  Thrust  two 

unmagnetized  knitting  needles  through  a  cork  at  right  angles  to  each 
other  (Fig.  351).  Support  the  apparatus  on  the  edges  of  two  glasses, 
with  the  axis  in  an  east-and-west  line,  and  the  needle  adjusted  so  as 
to  rest  horizontally.  Now  magnetize  the  needle,  being  careful  not  to 
displace  the  cork.  It  will  no  longer  assume  a  horizontal  position,  the 

north  pole  dipping  down  as  if  it  had  become 

heavier. 

The  inclination  or  dip  of  a  needle  is 
the  angle  its  magnetic  axis  makes  with 
a  horizontal  plane.  A  needle  mounted 
so  as  to  turn  about  a  horizontal  axis 
through  its  center  of  gravity  is  a  dip- 
ping needle  (Fig.  352).  The  dip  of 
the  needle  at  the  magnetic  poles  of  the 
earth  is  90°,  at  the  magnetic  equator, 
0°.  In  1907  Amundsen  placed  the 
magnetic  pole  of  the  northern  hemi- 
sphere in  latitude  75°  5' N.  and  longi- 
tude 96°47'W.  The  magnetic  pole 

of    the   southern   hemisphere   is   probably   near   latitude 

72°  S.  and  longitude  155°  E. 

Isoclinic  lines  are  lines  on  the  earth's  surface  passing 

through  points  of  equal  dip.     They  are  irregular  in  di- 


FIGURE  352.  —  DIPPING 
NEEDLE. 


338  MAGNETISM 

rection,  though   resembling  somewhat  parallels   of   lati- 
tude. 

404.  Magnetic  Declination.  —  The  magnetic  poles  of  the 
earth  do   not  coincide  with  the  geographical  poles,  and 
consequently  the  direction  of  the  magnetic  needle  is  not 
in  general  that  of  the  geographical  meridian.     The  angle 
between  the  direction  of  the  needle  and  the  meridian  at 
any  place  is  the  magnetic  decimation.     To  Columbus  be- 
longs the  undisputed  discovery  that  the  declination  is  dif- 
ferent at  different  points  on  the  earth's  surface.     In  1492 
he  discovered  a  place  of   no  declination  in  the  Atlantic 
Ocean  north  of  the  Azores.     The  declination  at  any  place 
is  not  constant,  but  changes  as  if  the  magnetic  poles  oscil- 
late, while  the  mean  position  about  which  they  oscillate 
is  subject  to  a  slow  change  of  long  period.     The  annual 
change  on  the  Pacific  coast  is  about  4',  and  in  New  Eng- 
land about  3'.     At  London  in  1657  the  magnetic  declina- 
tion  was   zero,   and   it   attained   its   maximum   westerly 
value  of  24°  in  1816  ;  in  1915  it  was  15°  19'  W. 

405.  Agonic  Lines.  —  Lines  drawn  through  places  where 
the  needle  points  true  north  are  called  agonic  lines.     In 
1910  the  agonic  line  in  North  America  ran  from  the  mag- 
netic pole  southward  across  Lake  Superior,  thence  near 
Lansing,  Michigan,  Columbus,  Ohio,  through  West  Vir- 
ginia and  South  Carolina,  and  it  left  the  mainland  near 
Charleston  on  its  way  to  the  magnetic  pole  in  the  south- 
ern hemisphere.     East  of  this  line  the  needle  points  west 
of  north  ;   west  of  it,  it  points  east  of  north.     Lines  pass- 
ing  through    places   of   the  same  declination   are  called 
isogonic  lines. 


QUESTIONS  339 

Questions 

1.  Given  a  bar  magnet  of  unmarked  polarity;  determine  which 
end  is  its  north  pole. 

2.  Out  of  a  group  of  materials,  how  would  you  select  the  mag- 
netic substances? 

3.  Given  two  bars  exactly  alike  in  appearance,  one  soft  iron  and 
the  other  hardened  steel.     Select  the  steel  one  by  means  of  magnetism. 

4.  Magnetize  a  long  darning  needle,  then  break  it  in  the  middle. 
Will  there  be  two  magnets,  each  with  one  pole  ? 

5.  How  would  you  magnetize  a  sewing  needle  so  that  the  eye  is 
the  north  pole  ? 

6.  What  effect  would  it  have  on  a  compass  to  place  it  within  an 
iron  kettle  ? 

7.  Will  an  iron  fence  post  standing  in  the  ground  have  any  in- 
fluence on  the  needle  of  a  surveyor's  compass  ? 

8.  Float  a  magnet  on  a  cork.     Will  the  earth's  magnetism  cause 
it  to  float  toward  the  earth's  magnetic  pole  ? 

9.  Is  the  polarity  of  the  earth's  magnetism  in  the  northern  hemi- 
sphere the  same  as  that  of  the  north  pole  of  a  magnet? 

10.  Suppose  you  wish  to  make  a  magnetic  needle.  If  it  is  bal- 
anced on  a  point  so  as  to  rest  in  a  horizontal  position  before  magnet- 
ization, will  it  rest  horizontally  after  it  is  magnetized  ? 


CHAPTER   XI 


ELECTROSTATICS 
I.   ELECTRIFICATION 

406.    Electrical  Attraction.  —  Rub  a  dry  flint  glass  rod  with  a 
silk  pad  and  bring  it  near  a  pile  of  pith  balls,  bits  of  paper,  or  chaff. 

They  will  at  first  be  at- 
tracted and  then  repelled 
(Fig.  353). 

The  simple  fact  that 
a  piece  of  amber  (a  fos- 
sil gum)  rubbed  with 
a  flannel  cloth  acquires 
the  property  of  at- 
tracting bits  of  paper, 
pith,  or  other  light 

bodies,  has  been  known  since  about  600  B.C.  ;  but  it  seems 
not  to  have  been  known  down  to  the  time  of  Queen  Eliza- 
beth that  any  bodies  except  amber  and  jet  were  capable  of 
this  kind  of  excitation.  About  1600  Dr.  Gilbert  dis- 
covered that  a  large  number  of  substances,  such  as  glass, 
sulphur,  sealing  wax,  resin,  etc.,  possess  the  same  peculiar 
property.  These  he  called  electrics  (from  the  Greek  word 
for  amber,  electron).  A  body  excited  in  this  manner  is 
said  to  be  electrified,  its  condition  is  one  of  electrification, 
and  the  invisible  agent  to  which  the  phenomenon  is  re- 
ferred is  electricity. 

340 


FIGURE  353.  —  ELECTRICAL  ATTRACTION. 


TWO  KINDS   OF  ELECTRIFICATION 


341 


407.    Electrical  Repulsion.  —  Suspend  several  pith  balls  from  a 
glass  hook  (Fig.  354).     Touch  them  with  an  electrified  glass  tube. 
They  are  at  first  attracted  but  they  soon  fly  away  from  the  tube  and 
from  one  another.     When  the  tube  is 
removed    to  a  distance,  the    balls  no 
longer  hang  side  by  side,  but  keep  apart 
for  some  little  time.     If  we  bring  the 
hand  near  the   balls    they  will   move 
toward  it  as  if  attracted,  showing  that 
the  balls  are  electrified. 


From  this  experiment  it  ap- 
pears that  bodies  become  elec- 
trified by  coming  in  contact  with 
electrified  bodies,  and  that  elec- 
trification may  show  itself  by  re- 
pulsion as  well  as  by  attraction. 


FIGURE  354.  —  ELECTRICAL 
REPULSION. 


408.    Attraction  Mutual.  —  Electrify  a  flint  glass  tube  by  fric- 
tion with  silk,  and  hold  it  near  the  end  of  a  long  wooden  rod  resting 
in  a  wire  stirrup  suspended  by  a  silk  thread  (Fig.  355).     The  sus- 
pended rod  is  attracted.    Now,  replace  the  rod  by  the  electrified  tube. 
When  the  rod  is  held  near  the  rubbed  end 
of  the  glass  tube,  the  latter  moves  as  if  at- 
tracted by  the  former. 

The  experiment  teaches  that  each 
body  attracts  the  other ;  that  is,  the 
action  is  mutual. 

409 .    Two  Kinds  of  Electrification.  — 

Rub  a  glass  tube  with  silk  arid  suspend  it 
as  in  Fig.  355.  Rub  a  second  glass  tube 
and  hold  it  near  one  end  of  the  suspended 
one.  The  suspended  tube  will  be  repelled.  Bring  near  the  sus- 
pended tube  a  rod  of  sealing  wax  rubbed  with  flannel.  The  suspended 
tube  is  now  attracted.  Repeat  these  tests  with  an  electrified  rod  of 
sealing  wax  in  the  stirrup  instead  of  the  glass  tube.  The  electrified 


FIGURE  355.  —  ATTRAC- 
TION MUTUAL. 


342 


ELECTROSTATICS 


sealing  wax  will  repel  the  electrified  sealing  wax,  but  there  will  be 
attraction  between  the  sealing  wax  and  the  glass  tube. 

The  experiment  illustrates  the  fact  that  there  are  two 
kinds  of  electrification:  one  developed  by  rubbing  glass 
with  silk,  and  the  other  by  rubbing  sealing  wax  with 
flannel.  To  the  former  Benjamin  Franklin  gave  the  name 
positive  electrification  ;  to  the  latter,  negative  electrification. 

It  appears  further  that  bodies  charged  with  the  same 
kind  of  electrification  repel  each  other,  and  bodies  charged 
with  unlike  electrifications  attract  each  other.  Hence  the 
law : 

Like  electrical  charges  repel  each  other ;  unlike  electri- 
cal charges  attract  each  otlwr- 

410.  The  Electroscope.  —  An  instrument  for  detecting  electri- 
fication and  for  determining  its  kind  is  called  an  electroscope.  Of  the 
many  forms  proposed  the  one  shown  in  section  in 
Fig.  356  is  typical.  The  indicating  system  consists 
of  a  rigid  piece  of  brass  B,  to  which  is  attached  a 
narrow  strip  of  gold, leaf  G.  This  system  is  supported 
by  a  block  of  sulphur  /,  which  in  turn  is  suspended 
by  a  rod  fitting  tightly  in  a  block  of  ebonite  E.  A 
charging  wire  W  passes  through  the  ebonite  and  is 
bent  at  right  angles  at  the  bottom.  By  rotating  the 
upper  bent  end  of  W,  the  arm  at  the  bottom  may  be 
brought  in  contact  with  the  brass  strip  for  charging. 
ELECTROSCOPE  Instead  of  a  ball  the  supporting  rod  may  end  in  a 
round  flat  plate.  When  the  instrument  has  flat 
glass  sides,  the  gold  leaf  may  be  projected  on  the  screen  with  a 
lantern. 


FIGURE  357.  —  PROOF  PLANE. 


411.  Charging  an  Electro- 
scope. —  To  charge  an  electroscope 
an  instrument  called  a  proof  plane 
is  needed.  It  consists  of  a  small  metal  disk  attached  to  an  ebonite 
handle  (Fig.  357).  To  use  it,  touch  the  disk  to  the  electrified  body 
and  then  apply  it  to  the  knob  of  the  electroscope.  The  angular 


CONDUCTORS  AND  NONCONDUCTORS  343 

separation  of  the  foil  from  the  stem  will  indicate  the  intensity  of  the 
electric  charge  imparted.  This  method  is  known  as  charging  by 
contact  in  distinction  from  charging  by  induction  to  be  described  later. 

412.  Testing    for   Kind    of   Electrification.  —  Charge  the 
electroscope,  by  means  of  the  proof  plane,  with  the  kind 
of  electrification  to  be  identified,  until  the  leaf  diverges  a 
moderate  distance.     Then  apply  a  charge  from  a  glass  rod 
electrified  by  rubbing  with  silk.     If  the  divergence  in- 
creases, the  first  charge  was  positive ;  if  not,  recharge  the 
electroscope  from  the  unknown  and  apply  a  charge  taken 
from  a  stick  of  sealing  wax  excited  by  friction  with  flan- 
nel.    No  certain  conclusion  can  be  drawn  unless  an  in- 
creased divergence  is  obtained. 

413.  Conductors  and  Nonconductors.  — Fasten  a  smooth  metal 
button  to  a  rod  of  sealing  wax  and  connect  the  button  with  the  knob 
of  the  electroscope  by  a  fine  copper  wire,  50  to  100  cm.  long.     Hold 
the  sealing  wax  in  the  hand  and  touch  the  button  with  an  electrified 
glass  rod.     The  divergence  of  the  leaf  indicates  that  it  is  electrified. 
Repeat  the  experiment,  using  a  silk  thread  instead  of  the  wire ;  no 
effect  is  produced  on  the  electroscope.     Now  wet  the  thread  with 
water  and  apply  the  electrified  rod ;  the  effect  is  the  same  as  when  the 
wire  was  used. 

It  is  clear  from  these  experiments  that  electric  charges 
pass  readily  from  one  point  to  another  along  copper  wire, 
but  do  not  pass  along  dry  silk  thread.  It  is  therefore  cus- 
tomary to  divide  substances  into  two  classes,  conductors 
and  nonconductors,  or  insulators,  according  to  the  facility 
with  which  electric  charges  pass  in  them  from  point  to 
point.  In  the  former  if  one  point  of  the  body  is  electrified 
by  any  means,  the  electrification  spreads  over  the  whole 
body,  but  in  a  nonconductor  the  electrification  is  confined 
to  the  vicinity  of  the  point  where  it  is  excited.  Sub- 
stances differ  greatly  in  their  conductivity,  so  that  it  is 


344 


ELECTROSTATICS 


not  possible  to  divide  them  sharply  into  two  classes. 
There  is  no  substance  that  is  a  perfect  conductor ;  neither 
is  there  any  that  affords  perfect  insulation.  Metals,  car- 
bon, and  the  solution  of  some  acids  and  salts  are  the  best 
conductors.  Among  the  best  insulators  are  paraffin,  tur- 
pentine, silk,  sealing  wax,  India  rubber,  gutta-percha,  dry 
glass,  porcelain,  mica,  shellac,  spun  quartz  fibers,  and 
liquid  oxygen.  Some  insulators,  like  glass,  become  good 
conductors  when  heated  to  a  semi-fluid  condition. 


II.   ELECTROSTATIC  INDUCTION 

414.  Electrification  by  Induction.  —  Rub  a  glass  tube  with  silk 
and  bring  it  near  the  top  of  an  electroscope.     The  leaves  begin  to 

diverge  when  the  tube  is  some  dis- 
tance from  the  knob  (Fig.  358)  and 
the  amount  of  divergence  increases 
•t  ;.>  :  as  the  tube  approaches.  When 
the  tube  is  removed  the  leaves  col- 


Since  the  leaves  do  not  re- 
main apart,  it  is  evident  that 
there  has  been  no  transfer  of 
electrification  from  the  tube 
to  the  electroscope.  The 
electrification  produced  in 
the  electroscope  when  the 
electrified  body  is  brought 
near  it  is  owing  to  electrostatic 
induction.  This  form  of  elec- 
trification is  only  a  temporary  one  and  it  is  brought  about 
by  the  presence  of  a  charged  body  in  its  vicinity. 

415.    Sign  of  the  Induced  Charges.  —  Lay  a  smooth  metallic 
ball  on  a  dry  plate  of  glass.     Connect  it  with  the  knob  of  the  electro- 


FIGURE  358.  —  ELECTRIFICATION   BY 
INDUCTION. 


EQUALITY  OF  THE  TWO   CHARGES 


345 


scope  by  means  of  a  stout  wire  with  an  insulating  handle  (Fig.  359). 
The  ball  and  the  electroscope  now  form  one  continuous  conductor. 
Bring  near  the  ball  an  electrified  glass  tube ;  the  leaves  of  the  elec- 
troscope diverge.  Before  with- 
drawing the  excited  tube,  remove 
the  wire  conductor.  The  electro- 
scope remains  charged,  and  it  will 
be  found  to  be  positive.  A  similar 
test  made  of  the  ball  will  show  that 
it  is  negatively  charged. 


o 


FIGURE  359.  —  WIRE  WITH  INSU- 
LATING HANDLE. 


Hence,  we  learn  that  when  an  electrified  body  is  brought 
near  an  object  it  induces  the  opposite  kind  of  electrification 
on  the  side  next  it  and  the  same  kind  on  the  remote  side. 


416.  Charging  an  Electroscope  by  Induction.  —  Hold  a  finger 
on  the  ball  of  the  electroscope  and  bring  near  it  an  electrified  glass 
tube  (Fig.  360) .  Remove  the  finger  before  taking  away  the  tube ;  the 

electroscope  will  be  charged 
negatively.  If  a  stick  of  elec- 
trified sealing  wax  be  used  in- 
stead of  the  glass  tube,  the 
electroscope  will  be  charged 
positively. 

417.  Equality  of  the  Two 
Charges.  —  Using  the  appa- 
ratus of  §  415,  charge  the 
ball  and  the  electroscope  by 
induction.  Then  replace  the 
wire  conductor.  The  leaves 
of  the  electroscope  will  col- 
lapse, showing  that  the  elec- 
troscope is  discharged.  If  the 

P.GURE   360. -CHARGING    ELECTROSCOPE    bal1    be    tested'    !t    wil1    als° 
BY  INDUCTION.  be   found   to    be    discharged. 

Hence, 

The  inducing  and  the  induced  charges  are  equal  to  each 
other. 


346 


ELECTROSTATICS 


III.   ELECTRICAL  DISTRIBUTION 

> 

418.   The  Charge  on  the  Outside  of  a  Conductor.  —  Place  a 
round   metallic  vessel  of  about  one  liter  capacity  on  an  insulated 

support  (Fig.  361).  Electrify 
strongly  and  test  in  succession 
both  the  inner  and  the  outer 
surface,  using  a  proof  plane  to 
convey  the  charge  to  the  electro- 
scope. The  inner  surface  will 
give  no  sign  of  electrification. 

Hence,  it  appears  that 
the  electrical  charge  of  a 
conductor  is  confined  to  its 
outer  surface. 


419.  Effect  of    Shape.— 

Charge  electrically  an  insulated 
egg-shaped  conductor  (Fig.  362). 
Touch  the  proof  plane  to  the 
large  end,  and  convey  the  charge 
to  the  electroscope.  Notice  the 
Test  the  side  and  the  small  end 
The  greatest  divergence  of  the 


FIGURE  361.  —  CHARGE  ON  OUTSIDE. 


amount  of  divergence  of  the  leaves. 

of  the  conductor  in  the  same  way. 

leaves  will  be  produced  by  the  charge  from  the  small 

end  and  the  least  from  the  sides. 


The  experiment  shows  that  the  surface 
density  is  greatest  at  the  small  end  of  the 
conductor. 

By  surface  density  is  meant  the  quantity 
of  electrification  on  a  unit  area  of  the  sur- 
face of  the  conductor. 


FIGURE  362.  — 
SURFACE  DENSITY 
DEPENDENT  ON 
CURVATURE. 


The  distribution  of  the  charge  is,  therefore, 
affected  by  the  shape  of  the  conductor,  the  surface  density 
"being  greater  the  greater  the  curvature. 


ACTION  OF  POINTS  347 

420.  Action  of  Points.  —  Attach  a  sharp-pointed  rod  to  one  pole  of 
an  electrical  machine  (§  433),  and  suspend  two  pith  balls  from  the  same 
pole.  When  the  machine  is  worked  there  will  be  little  or  no  separa- 
tion of  the  pith  balls.  Hold  a  lighted  candle 
near  the  pointed  rod;  the  candle  flame  will 
be  blown  away  as  by  a  stiff  breeze  (Fig.  363). 

The  experiment  shows  that  an  elec- 
tric charge  is  carried  off  by  pointed 
conductors.  This  conclusion  might 
have  been  drawn  from  the  preceding 
experiment.  When  the  curvature 

of  the  egg-shaped  conductor  becomes         FIGURE  363.  —  FLAME 
,,          ,,  /.          i  BLOWN   AWAY  BY   Dis- 

very  great   so   that  the  surface  be-      CHARQE  FROM  POINT 

comes  pointed,  the  surface  density 
also  becomes  great  and  there  is  an  intense  field  of  electric 
force  in  the  immediate  neighborhood.  The  air  particles 
touching  the  point  become  heavily  charged  and  are  then 
repelled ;  other  particles  take  their  place  and  are  in  turn 
repelled  and  form  an  electrical  wind.  The  conductor  gives 
up  its  charge  to  the  repelled  particles  of  air. 

Questions 

1.  When  a  charge  is  conveyed  by  a  proof  plane  to  an  electroscope, 
does  the  proof  plane  give  up  its  entire  charge  ? 

2.  Why  will  not  an  electroscope  remain  charged  indefinitely  ? 

3.  If  the  ball  of  an  electroscope  were  hollow  with  an  aperture  so 
that  the  charged  proof  plane  could  be  introduced,  would  any  charge 
remain  on  the  proof  plane  after  touching  the  inside  of  the  ball  ? 

4.  Will  dust  have  any  effect  on  the  working  of  electrical  apparatus  ? 

5.  Why  should  electrical  apparatus  be  warmer  than  the  room  if 
we  are  to  get  good  results  in  electrostatic  experiments  ? 

6.  Why  does  electrostatic  apparatus  wort  better  in  cold  weather 
than  in  warm  ? 

7.  Place  an  electroscope  in  a  cage  of  fine  wire  netting.     Why  is  it 
not  affected  by  an  electrified  glass  rod  held  near  it? 


348  ELECTROSTATICS 

8.  Why  does  not  a  metal  rod  held  in  the  hand  and  rubbed  with 
silk  show  electrification  ? 

9.  With  a  positively  charged  globe,  how  could  another  insulated 
globe  be  charged  without  reducing  the  charge  on  the  first  one? 

10.    In  charging  an  electroscope  by  induction,  why  must  the  finger 
be  withdrawn  before  removing  the  inducing  charge  ? 

IV.   ELECTRIC  POTENTIAL  AND  CAPACITY 

421.  The  Unit  of  Electrification  or  Charge.  — Imagine  two 
minute  bodies  similarly  charged  with  equal  quantities 
of  electricity.  They  will  repel  each  other.  If  the  two 
equal  and  similar  charges  are  one  centimeter  apart  in  air, 
and  if  they  repel  each  other  with  a  force  of  one  dyne, 
then  the  charges  are  both  unity.  The  electrostatic  unit  of 
quantity  is  that  quantity  which  will  repel  an  equal  and  similar 
quantity  at  a  distance  of  one  centimeter  in  air  with  a  force  of 
one  dyne.  It  is  necessary  to  say  "  in  air  "  because,  as  will 
be  seen  later,  the  force  between  two  charged  bodies  depends 
on  the  nature  of  the  medium  be- 
tween them  (§  427). 

This  electrostatic  unit  is  very 
small  and  has  no  name.  In  prac- 
tice, a  larger  unit,  called  the  coulomb, 
is  employed.  It  is  equal  to  3  x  109 
electrostatic  units. 

422.    Potential    Difference.  —  The 
analogy  between  pressure  in  hydro- 
statics and  potential  in  electrostatics 
FIGURE  364.- ILLUSTRATING    ig    ft  convenient    and    helpful 

POTENTIAL  DIFFERENCE.  / 

one.      W  ater  will  now  from  the  tank 

A  to  the  tank  B  (Fig.  364)  when  the  stopcock  S  in  the 
connecting  pipe  is  open  if  the  hydrostatic  pressure  at 
a  is  greater  than  at  b  ;  and  the  flow  is  attributed  directly 
to  this  difference  of  pressure. 


ZERO  POTENTIAL  349 

In  the  same  way,  if  there  is  a  flow  of  positive  electricity 
from  A  to  B  when  the  two  conductors  are  connected  by  a 
conducting  wire  r  (Fig.  365),  the  electrical  potential  is 
said  to  be  higher  at  A  than 
at  B,  and  the  difference  of 
electrical  potential  between 
A.  and  B  is  assigned  as  the 
cause  of  the  flow.  In  both  FIGURE  365.  —  CONDUCTOR  A  OF 
cases  the  flow  is  in  the  di-  ^"J*  P°TENT1AL  ™AN  C°NDUC- 
rection  of  the  difference  of 

pressure  or  difference  of  potential,  irrespective  of  the  fact 
that  B  may  already  contain  more  water  because  of  its 
large  cross  section,  or  a  greater  electric  charge  because  of 
its  larger  capacity  (§  425). 

If  the  electric  charge  in  a  system  of  connected  conduc- 
tors is  in  a  stationary  or  static  condition,  there  is  then 
no  potential  difference  between  different  points  of  the 
system. 

The  potential  difference  between  two  conductors  is  meas- 
ured by  the  work  done  in  carrying  a  unit  electric  charge 
from  the  one  to  the  other. 

423.  Unit  Potential  Difference.  —  There  is  unit  potential 
difference  between  two  conductors  when  one  erg  of  work 
is  required  to  transfer  the  unit  electric  charge  from  one 
conductor    to    the    other.      This    is    called    the    absolute 
unit ;  for  practical  purposes  it  has  been  found  more  con- 
venient to  employ  a  unit  of  potential  difference  (P.  D.), 
which  is  -%fa  of  the  absolute  unit,  and  which  is  called  the 
volt,  in  honor  of  the  Italian  physicist,  Alessandro  Volta. 

424.  Zero  Potential.  —  In  measuring  the  potential  differ- 
ence between  a  conductor  and  the  earth,  the  potential  of 
the  earth  is  assumed  to  be  zero.     The  potential  difference 
is  then  numerically  the  potential  of  the  conductor.      If  a 


350  ELECTROSTATICS 

conductor  of  positive  potential  be  connected  with  the 
earth  by  an  electric  conductor,  the  positive  charge  will 
flow  to  the  earth.  If  the  conductor  has  a  negative  poten- 
tial, the  flow  of  the  positive  quantity  will  be  in  the  other 
direction. 

425.  Electrostatic  Capacity.  —  If  water  be  poured  into  a 
cylindrical  jar  until  it  is  10  cm.  deep,  the  pressure  on  the 
bottom  of  the  jar  is  10  g.  of  force  per  square  centimeter. 
If  the  depth  of  the  water  be  increased  to  20  cm.,  the  pres- 
sure will  be  20  g.  of  force  per  square  centimeter  (§  53). 
It  thus  appears  that  there  is  a  constant  relation  between 
the  quantity  of  water  Q  and  the  pressure  P ;  that  is, 

.j£  =  (7,  a  constant. 

Again,  if  a  gas  tank  be  filled  with  gas  at  atmospheric  pres- 
sure, it  will  exert  a  pressure  of  1033  g.  of  force  per  square 
centimeter  (§  81).  If  twice  as  much  gas  be  pumped  into  the 
tank,  the  pressure  by  Boyle's  law  (§  87)  will  be  doubled 
at  the  same  temperature  ;  that  is,  there  is  a  constant  re- 
lation between  the  quantity  of  gas  Q  and  the  pressure  P 

of  the  gas  in  the  tank,  or  -^  =  (7,  a  constant  as  before. 

In  the  same  way,  if  an  electric  charge  be  given  to  an 
insulated  conductor,  its  potential  will  be  raised  above  that 
of  the  earth.  If  the  charge  be  doubled,  the  potential 
difference  between  the  conductor  and  the  earth  will  also 
be  doubled.  Precisely  as  in  the  case  of  the  water  and  of 
the  gas,  there  is  a  constant  relation  between  the  amount 
of  the  charge  Q  and  the  potential  difference  V  between 

the  conductor  and  the  earth  ;  that  is,  -j^=  O.     This  ratio 

or  constant  O  is  the  electrostatic  capacity  of  the  conductor. 
If  V=  1,  then  0  =  Q ;  from  which  it  follows  that  the 


INFLVENCE  OF  THE  DIELECTRIC  351 

electrostatic  capacity  of  a  conductor  is  equal  to  the  charge  re- 
quired to  raise  its  potential  from  zero  to  unity. 

From-;=  0  we  have#=  CV,  and  F=  -§•    (Equation  34) 


426.  Condensers.  —  Support  a  metal  plate  in  a  vertical  position 
on  an  insulating  base  (Fig.  366).     Connect  it  to  the  knob  of  an  elec- 
troscope by  a  fine  copper  wire.     Charge  the  plate  until  the  leaves  of 
the  electroscope  show  a  wide  divergence.     Now  bring  an  uninsulated 
conducting  plate  near  the  charged  one 

and  parallel  to  it.     The  divergence  of      „«„,        „.        _    Electroscope 
the  leaves  will   decrease;    remove  the 
uninsulated  plate   and  the  divergence 
will  increase  again. 

The  capacity  of   an  insulated 
conductor   is    increased   by    the 
presence    of    another    conductor       FIGURE  366.  —  CONDENSER 
connected  with  the  earth.     The 

effect  of  this  latter  conductor  is  to  decrease  the  potential 
to  which  a  given  charge  will  raise  the  insulated  one. 
Such  an  arrangement  of  parallel  conductors  separated  by 
an  insulator  or  dielectric  is  called  a  condenser. 

A.  condenser  is  a  device  which  greatly  increases  the 
charge  on  a  conductor  without  increasing  its  potential.  In 
other  words,  the  plate  connected  with  the  earth  greatly 
increases  the  capacity  of  the  insulated  conductor. 

427.  Influence  of  the  Dielectric.  —  Charge  the  apparatus  of  the 
last  experiment,  with  the  uninsulated  plate  at  a  distance  of  about 
5  cm.  from  the  charged  plate  and  parallel  to  it,  thrust  suddenly  be- 
tween the  two  a  cake  of  clean  paraffin  as  large  as  the  metal  plates  or 
larger,  and  from  2  to  4  cm.  thick.     Note  that  the  leaf  of  the  electro- 
scope (Fig.  356)  collapses  slightly.     Remove  the  paraffin  quickly,  and 
the  divergence  will  increase  again.     A  cake  of  sulphur  will  produce 
a  more  marked  effect  on  the  divergence  of  the  leaf. 


352 


ELECTROSTA  TICS 


FIGURE  367.  —  LEY- 
DEN  JAR. 


The  presence  of  the  paraffin  or  the  sulphur  increases 
the  capacity  of  the  condenser  and,  hence,  decreases  its 
potential,  the  charge  remaining  the  same. 
Paraffin  and  sulphur,  as  examples  of 
dielectrics,  are  said  to  have  a  larger 
dielectric  capacity  or  dielectric  constant 
than  air.  Glass  has  a  dielectric  capacity 
from  four  to  ten  times  greater  than 
air. 

428.  The  Leyden  Jar  is  a  common  and 
convenient  form  of  condenser.  It  con- 
sists of  a  glass  jar  coated  part  way  up, 
both  inside  and  outside,  with  tin-foil 
(Fig.  367).  Through  the  wooden  or 
ebonite  stopper  passes  a  brass  rod,  ter- 
minating on  the  outside  in  a  ball  and  on  the  inside  in  a 
metallic  chain  which  reaches  the  bottom  of  the  jar.  The 
glass  is  the  dielectric  separat- 
ing the  two  tin-foil  conduct- 
ing surfaces. 

429.  Charging  and  Discharg- 
ing a  Jar.  —  To  charge  a  Ley- 
den  jar  connect  the  outer 
surface  to  one  pole  of  an 
electrical  machine  (§  433), 
either  by  a  metallic  conductor 
or  by  holding  the  jar  in  the 
hand.  Hold  the  ball  against 
the  other  pole.  To  discharge  a  Leyden  jar  bend  a  wire 
into  the  form  of  the  letter  V.  With  one  end  of  the  wire 
touching  the  outer  surface  of  the  jar  (Fig.  368),  bring  the 
other  around  near  the  ball,  and  the  discharge  will  take 
place. 


FIGURE  368.  —  DISCHARGING  A 
LEYDEN  JAR. 


THEORY  OF  THE  LEYDEN  JAR 


353 


FIGURE    369.  —  SEAT 
OF  THE  CHARGE. 


430.  Seat  of  Charge.  —  Charge  a  Leyden  jar  made  with  movable 
metallic  coatings  (Fig.  369)  and  set  it  on  an  insulating  stand.     Lift 
out  the  inner  coating,  and  then,  taking  the  top  of  the  glass  vessel  in 
one  hand,  remove  the  outer  coating  with  the 

other.  The  coatings  now  exhibit  no  sign  of 
electrification.  Bring  the  glass  vessel  near  a 
pile  of  pith  balls ;  they  will  be  attracted  to  it, 
showing  that  the  glass  is  electrified.  Reacji 
over  the  rim  with  the  thumb  and  forefinger 
and  touch  the  glass.  A  slight  discharge  may 
be  heard.  Now  build  up  the  jar  by  putting 
the  parts  together ;  the  jar  will  still  be  highly 
electrified  and  may  be  discharged  in  the 
usual  way. 

This  experiment  was  devised  by 
Franklin  ;  it  seems  that  electrification 
is  a  phenomenon  of  the  glass,  and  that 
the  metallic  coatings  serve  merely  as  conductors,  making 
it  possible  to  discharge  all  parts  of  the  glass  at  once. 
Some  claim  that  the  moisture  condensed  on  the  glass  acts 
as  a  conductor  when  the  metallic  coatings  are  removed. 

431.  Theory  of  the  Leyden  Jar.  —  A  Leyden  jar   may  be 
perforated  by  overcharging,  may  be  discharged  by  heat- 
ing, and  if  heavily  charged  is  not  completely  discharged 
by  connecting  the  two  coatings  ;    if  left  standing  a  few 
seconds,   the    two    coatings    gradually   acquire    a    small 
potential  difference  and   a   second   small  discharge  may 
be  obtained,  known  as  the  residual  charge.     It   appears, 
therefore,  that  the  glass  of  a  charged  jar  is  strained  or 
distorted ;  like  a  twisted  glass  fiber,  it  does  not  return  at 
once  to  its  normal  state  when  released. 

The  two  surfaces  of  the  glass  are  oppositely  electrified, 
the  one  charge  acting  inductively  through  the  glass  and 
producing  the  opposite  electrification  on  the  other  surface. 
The  two  charges  are  held  inductively  and  are  said  to  be 


354  ELECTROSTATICS 

"  bound,"  in  distinction  from  the  charge  on  an  insulated 
conductor,  which  is  said  to  be  "free." 

Questions 

1.  Will  a  charged  Leyden  jar  be  discharged  by  touching  the  knob 
while  the  jar  rests  on  a  sheet  of  hard  rubber  ? 

2.  Will  a  Leyden  jar  be  appreciably  charged  by  applying  charges 
to  the  knob  while  the  jat  rests  on  a  sheet  of  hard  rubber? 

3.  In  discharging  a  Leyden  jar  with  a  bent  wire,  why  not  touch 
the  wire  to  the  knob  before  touching  the  outside  surface  ? 

4.  Cuneus  tried  to  charge  a  bowl  of  water  by  holding  it  in  his 
hand,  while  the  chain  of  an  electrical  machine  dipped  into  the  water. 
When  he  lifted  the  chain  with  the  other  hand  he  got  a  shock.     Why? 

5.  Explain  why  a  small  metal  ball  suspended  by  a  silk  thread 
between  two  bodies,  the  two  being  near  together  and  charged,  one 
negatively  and  the  other  positively,  flies  back  and  forth  between  the 
two  bodies. 

V.   ELECTRICAL  MACHINES 

432.  The  Electrophorus.  —  The  simplest  induction  elec- 
trical machine  is  the  electrophorus  (Fig.  370),  invented  by 

Volta.  A  cake  of  resin  or 
disk  of  vulcanite  A  rests  in 
a  metallic  base  B.  Another 
metallic  disk  or  cover  C  is 
provided  with  an  insulating 
handle  D.  The  resin  or  vul- 
canite is  electrified  by  rub- 
bing with  dry  flannel  or 
striking  with  a  catskin,  and 

the  metal  disk  is  then  placed 
FIGURE  370.  —  ELECTROPHORUS.  .,          0.  ,, 

on   it.      Since  the  cover 

touches  the  nonconducting  resin  or  vulcanite  A  in  a  few 
points  only,  the  negative  charge  due  to  the  friction  is 
not  removed.  The  two  disks  with  the  film  of  air  be- 
tween them  form  a  condenser  (§  426)  of  great  capacity. 


INFLUENCE  ELECTRICAL  MACHINES  355 

Touch  the  cover  momentarily  with  the  finger,  and  the  repelled 
negative  charge  passes  to  the  earth,  leaving  the  cover  at  zero  poten- 
tial. Lift  it  by  the  insulating  handle,  the  positive  charge  becomes 
free  (§  431),  and  a  spark  may  be  drawn  by  holding  the  finger  near  it. 
This  operation  may  be  repeated  an  indefinite  number  of  times  with- 
out sensibly  reducing  the  charge  on  the  vulcanite. 

When  the  cover  is  lifted  by  the  insulating  handle,  work 
is  done  against  the  electrical  attraction  between  the  nega- 
tive charge  on  the  vulcanite  and  the  positive  on  the  cover. 
The  energy  of  the  charged  cover  represents  this  work. 

The  electrophorus  is,  therefore,  a  device  for  transforming 
energy  in  some  other  form  into  the  energy  of  electric  charges. 

433.  Influence  Electrical  Machines.  —  There  are  many  in- 
fluence or  induction  electrical  machines,  but  it  will  suffice 
to  describe  only  one,  as  the  principle  is  always  the  same. 


FIGURE  371.  —  TOEPLER-HOLTZ  MACHINE. 

The  Holtz  machine,  as  modified  by  Toepler  and  Voss, 
is  illustrated  in  Fig.  371.  There  are  two  glass  plates,  e1 
and  e,  about  5  mm.  apart,  the  former  stationary  and  the 


356 


ELECTED  ST A  TICS 


latter  turning  about  an  insulated  axle  by  means  of  the 
crank  h  and  a  belt.  The  stationary  plate  supports  at  the 
back  two  paper  sectors,. c  and  <?',  called  armatures.  Be- 
tween them  and  the  stationary  plate  ef  are  disks  of  tin-foil 
connected  by  a  narrow  strip  of  the  same  material.  '  The 
disks  are  electrically  connected  with  two  bent  metal  arms, 
a  and  af  (opposite  a),  which  carry  at  the  other  end  tin- 
sel brushes  long  enough  to  rub  against  low  brass  buttons 
cemented  to  small  tin-foil  disks,  called  carriers,  on  the 
front  of  the  revolving  plate.  Opposite  the  paper  sectors 
and  facing  them  are  two  metal  rods  with  several  sharp- 
pointed  teeth  set  close  to  the  revolving  plate,  but  not 
touching  the  metal  buttons  and  carriers.  The  diagonal 
neutralizing  rod  d  has  tinsel  brushes  in  addition  to  the 
sharp  points.  The  two  insulated  conductors,  terminating 
in  the  balls,  m  and  w,  have  their  capacity  increased  by  con- 
nection with  the  inner  coating  of 
two  small  Leyden  jars,  i  and  i' ; 
the  outer  coatings  are  connected 
under  the  base  of  the  machine. 

There  are  so  many  varieties  of 
induction  machines,  and  the  ex- 
planation of  their  operation  is  so 
involved  and  uncertain,  that  we 
shall  leave  it  for  those  interested 
in  the  subject  to  look  it  up  in 
special  books  on  electricity. 


FIGURE  372.  —  BELLS  RUNG 
BY  ELECTRIFICATION. 


434.   Experiments  with  Electrical 

Machines.  —  1.    Attraction  and  repulsion. 

Place  a  number  of  bits  of  paper  on  the 

cover  of  a  charged  electrophorus.     Lift  it  by  the  insulating  handle. 
The  charged  pieces  of  paper  fly  off  <  he  plate. 

Three  bells   are   suspended  from  a  metal   bar  (Fig.  372).     The 


EXPERIMENTS    WITH  ELECTRICAL  MACHINES    357 


FIGURE  373.  —  ELECTRI- 
CAL TOURNIQUET. 


middle  one  is  insulated  from  the  bar ;  the  others  are  suspended  by 
chains.  Connect  the  bar  to  one  pole  of  an  electrical  machine  and  the 
middle  bell  to  the  other.  The  small  brass  balls  between  the  bells  are 
suspended  by  silk  cords;  they  swing  to  and 
fro  between  the  bells,  carrying  positive  charges 
in  one  direction  and  negative  in  the  other. 
This  apparatus,  called  the  electrical  chimes, 
is  of  interest  because  it  was  employed  by 
Franklin  in  his  lightning  experiments  to  an- 
nounce the  electrification  of  the  cord  leading 
to  the  kite  (§  435). 

2.  Discharge  by  points.     Connect  an  electri- 
cal tourniquet  (Fig.  373)  to  one  of  the  con- 
ductors of  an  electrical  machine,  the  other  con- 
ductor being  grounded.     When  the  machine 
is  turned,  the  whirl  rotates  rapidly  (§  420). 

3.  Mechanical  effects.     Hold  a  piece  of  cardboard  between  the  dis- 
charge balls  of   an  electrical  machine.     It  will  be  perforated  by  a 
spark  and  the  holes  will  be  burred  out  on  both  sides.     A  thin  dry 
glass  plate,  or  a  thin  test  tube  over  a  sharp  point,  may  be  perforated 
by  a  heavy  discharge. 

4.  Heating  effects.     Charge  a  Ley  den  jar  and  connect  its  outer  coat- 
ing with  a  gas  burner  by  a  chain  or  wire.     Turn  on  the  gas  and  bring 
the  ball  of  the  jar  near  enough  to  the  opening  in  the  burner  to  allow 

a  spark  to  pass.     The  gas  will  be  lighted 
by  the  discharge. 

Fill  a  gas  pistol  with  a  mixture  of  coal 
gas  and  air.  Discharge  a  Leyden  jar 
through  the  mixture.  It  will  explode 
and  the  cork  or  ball  will  be  shot  out  with 
some  violence. 

Magnetic  effects.  Wind  insulated  cop- 
per wire  around  a  small  glass  tube  (Fig. 
374),  and  place  inside  the  tube  a  piece 
of  darning  needle.  Discharge  a  Leyden 
jar  through  the  wire.  The  needle  will 
be  magnetized.  A  similar  effect  may  be 
produced  by  placing  a  large  sewing  needle  across  a  strip  of  tin-foil 
forming  a  part  of  the  discharge  circuit  of  a  Leyden  jar. 


FIGURE  374.  —  NEEDLE 
MAGNETIZED  BY  ELECTRIC  DIS- 
CHARGE. 


358  ELECTR  OSTA  TICS 


VI.   ATMOSPHERIC  ELECTRICITY 

435.  Lightning.  —  Franklin  demonstrated  in  1752  tha.t 
lightning  is  identical  with  the  electric  spark.  He  sent  up 
a  kite  during  a  passing  storm,  and  found  that  as  soon  as 
the  hempen  string  became  wet,  long  sparks  could  be  drawn 

from  a  key  attached  to 
it,  Leyden  jars  could  be 
charged,  and  other  effects 
characteristic  of  static 
electrification  could  be 
produced.  The  string 
was  not  held  in  the  hand 
directly,  but  by  a  silk 
ribbon  tied  to  it  for 
safety. 

Lightning  flashes  are 
discharges  between  op- 
positely charged  bodies. 
They  occur  either  be- 
tween two  clouds  or 

between  a  cloud  and  the 
FIGURE  375.  —  LIGHTNING  DISCHARGE.  ,,      XT7l.       OTC-\        T»U~ 

earth    (Fig   375).      I  he 

rise  of  potential  in  a  cloud  causes  a  charge  to  accumulate 
on  the  earth  beneath  it.  If  the  stress  in  the  air  reaches  a 
value  of  about  400  dynes  per  square  centimeter,  the  air 
breaks  down,  or  is  ruptured,  like  any  other  dielectric,  and 
the  two  opposite  charges  unite  in  a  long  zigzag  flash.  A 
lightning  flash  allows  the  strained  medium  to  return  to 
equilibrium.  The  coming  together  of  the  air  surfaces, 
which  are  separated  in  the  rupture,  produces  a  violent 
crash  of  thunder.  If  the  path  of  the  flash  be  long  and 
zigzag,  the  observer  will  hear  successive  sounds  from  differ- 


Benjamin  Franklin  (1706-1790)  was  born  at  Boston,  Massa- 
chusetts. In  his  twentieth  year  he  was  apprenticed  to  his  elder 
brother  in  the  printing  business.  When  forty  years  of  age  he  saw 
some  electrical  experiments  performed  with  a  glass  tube.  These 
excited  his  curiosity  and  he  began  experimenting  for  himself.  In 
less  than  a  year  he  had  discovered  the  discharging  effects  of  points 
and  worked  out  a  theory  of  electricity,  known  as  the  "  one-fluid 
theory."  He  explained  the  charged  Leyden  jar,  established  the 
identity  of  lightning  and  the  electric  spark,  invented  an  electric 
machine,  and  introduced  the  lightning  rod  as  a  protection  against 
lightning.  He  was  distinguished  as  a  statesman,  diplomatist,  and 
scientist.  He  founded  the  American  Philosophical  Society  and 
the  University  of  Pennsylvania. 


THE  LIGHTNING  ROD 


359 


ent  parts  of  the  path  as  a  crackling  rattle  ;  then  the  echoes 
from  other  clouds  will  come  rolling  in  afterwards.  The 
duration  of  a  lightning  flash  is  never  more  than  f  g^V<nr 
of  a  second.  If  it  lasted  much  longer,  its  intensity  is  so 
great  that  it  would  be  blinding. 

436.  The  Lightning  Rod.  —  Support  two  round  metal  plates, 
T  and  T',  one  above  the  other  and  a  few  centimeters  apart  (Fig. 
376).  The  upper  plate 
must  be  carefully  insulated  A 

except  from  the  pole  of  the 
electrical  machine  and  the 
inner  coating  of  a  Leyden 
jar  L.  Two  of  the  short 
rods  on  the  lower  plate 
terminate  in  small  balls; 
the  other  and  shortest  one 
is  pointed.  When  the  ma- 
chine is  worked,  the  ten- 
sion between  the  plates 
increases,  but  it  is  difficult  to  make  a  spark  pass ;  if  one  does  pass,  it 
will  strike  the  pointed  rod.' 

The  experiment  illustrates  the  protection  afforded  by  a 
pointed  conductor. 

A  lightning  rod  should  conform  to  the  following 
requirements : 

First.  It  should  be  perfectly  continuous,  of  sufficient 
size  to  resist  fusion,  and  made  preferably  of  strands  of 
wire  twisted  together  as  a  cable.  Iron  cables  are  as  good 
as  copper  ones. 

Second.  The  upper  end  should  terminate  in  points  and 
should  be  higher  than  adjacent  parts  of  the  building. 
The  lower  end  should  pass  down  into  the  earth  until  it 
enters  a  moist  conducting  stratum. 

Third.  The  rod  should  be  fastened  to  the  building 
without  insulators,  and  all  metal  parts  of  the  roof  should 


FIGURE  376.  —  PROTECTION  BY  POINTED 
ROD. 


360  ELECTROSTATICS 

be  connected  with  the  main  conductor.  It  is  better  to 
have  two  or  three  descending  rods  than  one,  and  all  the 
points  and  rods  should  be  connected  together  as  a  network. 
The  protection  afforded  by  lightning  rods,  properly 
erected,  is  abundantly  proven  by  the  statistics  of  mutual 
fire  insurance  companies  for  buildings  in  the  country. 

437.  Oscillatory   Discharge.  —  When  a   Leyden   jar  is  highly 
charged,  the  potential  difference  between  its  coatings  increases  until 
the  dielectric  between  the  discharge  terminals  suddenly  breaks  down 
and  a  spark  passes.     This  discharge  usually  consists  of  several  oscilla- 
tions or  to-and-fro  discharges,  like  the  vibrations  of  an  elastic  system 
or  the  surges  of  a  mass  of  water  after  sudden  release  from  pressure. 
Imagine  a  tank  with  a  partition  across  the  middle  and  filled  on  one 
side  with  water.     If  a  small  hole  be  made  in  the  partition  near  the 
bottom,  the  water  will  slowly  reach  the  same  level  on  both  sides  with- 
out agitation;   but  if  the  partition  be  suddenly  removed,  the  first 
violent  subsidence  will  be  succeeded  by  a  return  surge,  and  the  to-and- 
fro  motion  of  the  water  will  continue  with  decreasing  violence  until 
the  energy  is  all  expended. 

A  series  of  similar  surges  occurs  when  a  condenser  is  suddenly  dis- 
charged by  the  breaking  down  of  the  dielectric.  The  oscillatory  char- 
acter of  such  electric  discharges  was  discovered  by  Joseph  Henry  in 
1842.  Its  importance  has  been  recognized  only  in  recent  times.  Simi- 
lar electric  oscillations  probably  take  place  in  some  lightning  flashes. 

438.  The  Aurora.  —  The  aurora  is  due  to  silent  discharges 
in  the  upper  regions  of  the  atmosphere.     Within  the  arctic 
circle  it  occurs  almost  nightly,  and  sometimes  with  in- 
describable splendor.     The  illumination  of  the  aurora  is 
due  to  positive  discharges  passing  from  the  higher  regions 
of   the  atmosphere  to  the  earth,     In  our  latitude  these 
silent  streamers  in  the  atmosphere  are  infrequent.     When 
they  do  occur  they  are  accompanied  by  great  disturbances 
of  the  earth's  magnetism  and  by  earth  currents.     Such 
magnetic  disturbances  sometimes  occur  at  the  same  time 
in  widely  separated  portions  of  the  earth. 


CHAPTER   XII 

ELECTRIC  CURRENTS 

I.  VOLTAIC  CELLS 

439.  An  Electric  Current.  —  The  discharge  of  a  condenser 
through  a  wire  produces  in  and  around  the  wire  a  state 
called  an  electric  current.     If  by  any  arrangement  elec- 
tricity could  be  supplied  to  the  condenser  as  .fast  as  it  is 
conveyed  away  through  the  wire,  a  continuous  current 
would  be  produced.     Any  arrangement  by  which  the  ends 
of  a  conducting  wire  are  kept  at  different  potentials  will 
insure  the  flow  of  a  continuous  current  through  it. 

It  is  analogous  to  the  flow  of  heat  through  a  metal  rod 
if  one  end  is  kept  at  a  higher  temperature  than  the  other, 
the  heat  flowing  from  the  hotter  to  the  colder  end.  So  also 
a  stream  of  water  flows  through  a  section  of  pipe  if  the 
pressure  at  one  end  is  maintained  higher  than  at  the  other. 
It  is  customary  to  consider  the  electric  current  as  flowing 
from  positive  to  negative,  that  is,  from  higher  potential 
to  lower. 

One  of  the  simplest  means  of  maintaining  a  potential 
difference  between  the  terminals  of  a  conductor  is  the 
primary  or  voltaic  cell. 

440.  The  Voltaic  Cell.  —  Support  a  heavy  strip  of  zinc  and  one 
of  sheet  copper  (Fig.  377)  in  dilute  sulphuric  acid  (one  part  acid  to 
twenty  of  water).     After  the  zinc  has  been  in  the  acid  a  short  time, 
it  should  be  amalgamated  by  rubbing  it  with  mercury.     There  will  be 
no  apparent  change  when  the  plates  are  replaced  in  the  acid,  until 

361 


362 


ELECTRIC  CURRENTS 


the  two  are  connected  with  a  copper  wire ;  a  multitude  of  bubbles  of 
hydrogen  gas  will  then  immediately  be  given  off  at  the  surface  of  the 
copper  plate.  The  action  ceases  as  soon  as  the  wires  are  discon- 
nected. If  the  action  is  continued  for  some 
time,  the  zinc  will  waste  away,  while  the 
copper  is  not  affected. 

Such  a  combination  of  two  con- 
ductors, immersed  in  a  compound 
liquid,  called  an  electrolyte,  which  is 
capable  of  reacting  chemically  with 
one  of  the  conductors,  is  called  a 
voltaic  cell.  The  name  is  derived 
from  Volta  of  Padua,  who  first  de- 
scribed such  a  cell  in  1800. 


FIGURE  377. —  VOLTAIC 
CELL. 


441.  Plates  Electrically  Charged.  —  In  a  condensing  electro- 
scope the  ball  at  the  top  is  replaced  by  a  brass  disk  coated  with  thin 
shellac  varnish  as  an  insulator.  Resting  on 
it  is  a  second  disk  to  which  is  fitted  an  insu- 
lating handle.  The  two  disks  with  the  shellac 
varnish  between  them  form  a  condenser  of 
considerable  capacity. 

Connect  the  wire  leading  from  the  copper 
plate  of  two  or  three  voltaic  cells  C  in  series 
(§  473)  to  the  lower  disk  A  of  the  electro- 
scope, and  the  wire  from  the  zinc  plate  to  the 
upper  disk  B  (Fig.  378) .  Disconnect  the  wires, 
handling  them  one  at  a  time  by  means  of  a 
good  insulator  so  as  not  to  discharge  the  con- 
denser, and  then  lift  the  top  disk.  The  leaf 
L  of  the  electroscope  will  diverge,  and  a  test 
with  an  electrified  glass  rod  will  show  that  the 
electroscope  is  charged  positively. 


FIGURE  378.  —  PLATES 


This  posi-   OF     A     VOLTAIC     CELL 
CHARGED. 


tive  charge  was  derived  from  the  copper  strip 

of  the  cell.     Repeat  the  experiment  with  the  zinc  plate  connected 

to  the  lower  disk;  the  result  will  be  a  negative  charge  on  the  gold 

leaf. 


ELECTROCHEMICAL  ACTIONS  IN   VOLTAIC  CELL      363 

It  is  clear  from  this  experiment  that  the  plates  of  a  vol- 
taic cell  and  the  wires  leading  from  them  are  electrically 
charged,  the  copper  positively  and  the  zinc  negatively.  The 
conducting  rods,  plates,  or  cylinders  in  a  voltaic  cell  are 
called  electrodes,  the  copper  the  positive  electrode  and  the 
zinc  the  negative  electrode.  The  electric  current  leaves 
the  electrolyte  by  the  positive  electrode  and  enters  it  by 
the  negative. 

442.  The  Circuit.  —  The  circuit  of   a   voltaic    cell   com- 
prises the  entire  path  traversed  by  the  current,  including 
the  electrodes  and  the  liquid  in  the  cell  as  well  as  the  ex- 
ternal conductor.      Closing  the  circuit  means  joining  the 
two  electrodes  by  a  conductor  ;  breaking  or  opening  the  cir- 
cuit is  disconnecting  them.     So  when  the  circuit  is  broken 
at  any  point  by  a  key,  a  switch,  or  a  push  button,  the  cir- 
cuit is  said  to  be  open ;  when  the  key  or  switch  is  closed, 
so  as  to  make  a  continuous  path  for  the  current,  the  circuit 
is  said  to  be  closed.     The  flow  of  current  in  the  external 
circuit   is   from   the   positive   electrode  (copper)   to   the 
negative  (zinc),  and  in  the  internal  part  of  the  circuit 
from  the  negative  electrode  to  the  positive  (Fig.  377). 

443.  Electrochemical   Actions    in    a    Voltaic    Cell.  —  The 
theory  of   dissociation  furnishes   an    explanation  of   the 
manner  in  which  an  electric  current  is  conducted  through 
a  liquid.     It  is  briefly  as  follows  :     When  a  chemical  com- 
pound such  as  sulphuric  acid  (H2SO4),*  for  example,  is 

dissolved  in  water,  some  of  the  molecules  at  least  split  into 

++ 

two  parts  (H2  and  SO4),  one  part  having  a  positive  elec- 
trical charge  and  the  other  a  negative  one. 

The  two  parts  of  the  dissociated  substance  with  their 


*  Each  molecule  of  sulphuric  acid  is  composed  of  two  atoms  of  hydrogen 
(H2),  one  of  sulphur  (S),  and  four  of  oxygen  (O4). 


364 


ELECTRIC  CURRENTS 


Cu 


Zn 


electrical  charges  are  called  ions  (from  a  Greek  word 
meaning  to  go).  An  electrolyte  is  a  compound  capable  of 
such  dissociation  into  ions.  It  conducts  electricity  only 
by  means  of  the  migration  of  the  ions  resulting  from  the 
splitting  in  two  of  the  molecules.  The  separated  ions 
convey  their  charges  with  a  slow  and  measurable  velocity 
through  the  liquid.  Electropositive  ions,  such  as  zinc  and 
hydrogen,  carry  positive  charges  in  one  direction,  electro- 
negative ions,  such  as  "sulphion"  (SO4),  carry  negative 

charges  in  the  opposite  direction, 

t ^  and  the  sum  of  the  two  kinds  of 

charges  carried  through  the  liquid 
per  second  is  the  measure  of  the 
current. 

Figure   379  represents  a   sec- 
tion of   a  voltaic   cell  with  the 
electropositive     and    electroneg- 
^___________    ative     ions.       When     the     cir- 

FIGURE  379.— SECTION  OF  CELL  cuit    is     closed    and    a    current 

WITH  IONS.  flows,  zinc  from   the  zinc   plate 

++ 
enters  the  solution  as  electropositive  ions  (Zn),  while  the 

positive  hydrogen  ions  migrate  toward  the  copper  plate  or 
cathode,  and  the  sulphions  toward  the  zinc  plate.  The 
SO4  ions  carry  negative  charges  to  the  zinc  plate,  so  that 
it  becomes  charged  negatively,  while  the  H2  ions  carry 
positive  charges  to  the  copper  plate  and  it  becomes 
charged  positively.  Zinc  from  the  zinc  plate  thus  goes 
into  solution  as  zinc  sulphate  (ZnSO4),  and  hydrogen 
when  it  has  given  up  its  positive  charge  is  set  free  as 
gaseous  hydrogen  on  the  copper  plate.  Some  prefer  to 
say  that  when  the  zinc  ions  with  their  positive  charge 
leave  the  zinc  plate,  the  equivalent  negative  is  left  behind 


DIFFERENCE  OF  POTENTIAL 


365 


to  charge  the  zinc  electrode.  The  zinc  ions  unite  with 
the  sulphions  to  form  neutral  zinc  sulphate.  Thus,  while 
the  zinc  ions  are  electropositive  and  carry  positive  charges, 
the  zinc  plate  is  charged  negatively. 

444.  Electromotive    Force.  —  Imagine    a    rotary    pump 
which  produces  a  difference  of  pressure  between  its  inlet 
and  its  outlet.     Such  a  pump  may  cause  water  to  circulate 
through  a  system  of  horizontal  pipes  against  friction.     In 
any  portion  of  the  pipe  system  the  force  producing  the 
flow  is  the  difference  of  water  pressure  between  the  ends 
of  that  portion.     But  the  force  is  all  applied  at  the  pump, 
and  this  produces  a  pressure  throughout  the  whole  circuit. 
A  voltaic  cell  is  an  electric  generator  analogous  to  such  a 
pump. 

A  voltaic  cell  generates  electric  pressure  called  electro- 
motive force.  It  does  not  generate  electricity  any  more 
than  the  pump  generates  water,  but  it  sup- 
plies the  electric  pressure  to  set  electricity 
flowing.  This  electromotive  force  (E.M.F.) 
is  numerically  equal  to  the  work  which  must 
be  done  to  transport  a  unit  quantity  of  elec- 
tricity around  the  external  circuit  from  A  to 
£,  through  the  zinc  plate  to  Z,  from  Z 
through  the  liquid  (7,  and  thence  back  to  A 
(Fig.  380).  Work  is  done  in  this  transfer, 
because  all  conductors  offer  resistance  to  the 
passage  of  a  current.  The  energy  thus  ex- 
pended goes  to  heat  the  conductor.  A  vol- 
taic cell  is  thus  a  device  for  transforming  chemical  energy 
•into  the  energy  of  an  electric  current. 

445.  Difference  of  Potential.  —  The  difference  of  poten- 
tial between  two  points,  A  and  B,  on  the  external  conduct- 
ing circuit  is  the  work  done  in  carrying  a  unit  quantity  of 


FIGURE  380. 
—  CIRCUIT 
THROUGH  VOL- 
TAIC CELL. 


366 


ELECTRIC  CURRENTS 


electricity  from  the  one  point  to  the  other.  The  difference 
of  potential  between  the  electrodes  of  a  voltaic  cell  when 
the  circuit  is  closed  is  less  than  the  E.M.F.  of  the  cell  by 
the  work  done  in  transferring  unit  quantity  of  electricity 
through  the  electrolyte.  If  E  denotes  this  potential  dif- 
ference and  Q  the  quantity  conveyed,  then  the  whole  work 
done  is  the  product  EQ.  But  the  quantity  conveyed  by 
a  conductor  per  second  is  called  the  strength  of  current,  I. 
The  energy  transformed  in  a  conductor,  therefore,  when 
current  I  flows  through  it,  under  an  electric  pressure  or 
potential  difference  of  E  units  between  its  ends,  is  El  ergs 
per  second. 

446.  Detection  of  Current.  —  Solder  a  copper  wire  to  each  of 
the  strips  of  a  voltaic  cell,  and  connect  the  wires  with  some  form  of 

key  to  close  the  circuit. 
Stretch  a  portion  of  the 
wire  over  a  mounted 
magnetic  needle  (Fig. 
381)  f  holding  it  paral- 
lel to  it  and  as  near  as 
possible  without  touch- 
ing. Now  close  the 
circuit ;  the  needle  is 
deflected,  and  comes  to* 

rest,  at  an  angle  with  the  wire.  Next  form  a  rectangular  loop  of  the 
wire,  and  place  the  needle  within  it.  A  greater  deflection  is  now  ob- 
tained. If  a  loop  of  several  turns  is  formed,  the  deflection  is  still 
greater. 

A  magnetic  needle  employed  in  this  way  becomes  a 
galvanoscope,  a  detector  of  electric  currents.  This  experi- 
ment, first  performed  by  Oersted  in  1819,  shows  that  the 
region  around  the  wire  has  magnetic  properties  during  the 
flow  of  electricity  through  the  wire.  In  other  words,  it  is 
a  magnetic  field  (§  398), 


FIGURE  38 1 .  —  DEFLECTION  OF  NEEDLE  BY  CURRENT. 


Hans  Christian  Oersted  (1777-1851)  was  born  at  Rudkjo- 
bing,  Denmark,  and  received  his  education  at  the  University  of 
Copenhagen,  afterward  becoming  professor  in  the  University  and 
polytechnic  school  of  that  city.  It  was  while  holding  this  posi- 
tion that  he  discovered  the  action  of  the  electric  current  on  the 
magnetic  needle,  thus  establishing  the  connection  between  elec- 
tricity and  magnetism  which  had  long  been  sought  by  scientists. 
He  also  discovered  that  this  magnetic  action  of  the  electric  cur- 
rent takes  place  freely  through  a  great  many  substances.  Oersted 
wrote  extensively  for  newspapers  and  magazines  in  an  endeavor 
to  make  science  popular. 


LOCAL   ACTION  367 

447.  Relation  b:tween  the  Direction  of  the  Current  and  the 
Direction  of  Deflection.  —  Making  use  of  the  apparatus  of  §  44:6, 
compare  the  direction  of  the  current  through  the  wire  with  that  in 
which  the  north  pole  of  the  needle  turns.     Cause  the  current  to  pass 
in  the  reverse  direction  over  the  needle;  the  deflection  is  reversed. 
Now  hold  the  wire  below  the  needle,  and  the  direction  of  deflection  is 
again  reversed  as  compared  with  the  deflection  when  the  wire  is  held 
above  the  magnetic  needle. 

The  direction  of  the  deflection  may  always  be  predicted 
by  the  following  rule  :  Stretch  out  the  right  hand  along  the 
wire,  with  the  palm  turned 
toward  the  magnetic  needle, 
and  with  the  current  flowing 
in  the  direction  of  the  ex- 
tended fingers.  The  out- 
stretched thumb  will  then 
point  in  the  direction  in  F'°«<*  382.- D,*ECT,ON  OF  DEFLECTS. 

which  the  north  pole  of  the  needle  is  deflected  (Fig.  382). 
By  the  converse  of  this  rule,  the  direction  of  the  current 
may  be  inferred  from  the  direction  in  which  the  needle 
is  deflected. 

448.  Local  Action.  —  Place  a  strip  of  commercial  zinc  in  dilute 
sulphuric  acid.     Hydrogen  is  liberated  during  the  chemical  action, 
and  after  a  few  minutes  the  zinc  becomes  black  from  particles  of  car- 
bon exposed  to  view  by  dissolving  away  the  surface.     If  the  experi- 
ment is  repeated  with  zinc  amalgamated  with  mercury,  that  is,  by 
coating  it  with  an  alloy  of  mercury  and  zinc,  there  will  be  little  or  no 
chemical  action.     A  strip  of  chemically  pure  zinc  acts  much  like  one 
amalgamated  with  mercury. 

Thus  we  see  that  the  amalgamation  of  commercial  zinc 
with  mercury  changes  its  properties.  If  in  the  experiment 
with  the  simple  voltaic  cell,  a  galvanoscope  is  inserted  in 
the  circuit  both  before  the  zinc  has  been  amalgamated  and 


368 


ELECTRIC  CURRENTS 


afterward,  it  will  be  found  that  a  larger  deflection  will  be 
obtained  in  the  second  case. 

In  a  voltaic  cell  the  chemical  action  which  contributes 
nothing  to  the  current  flowing  through  the  circuit  is 
known  as  local  action.  It  is  probably  due  to  the  presence 
of  carbon,  iron,  etc.,  in  the  zinc ;  these  with  the  zinc  form 
miniature  voltaic  cells,  the  currents  flowing  around  in  short 
circuits  from  the- zinc  through  the  liquid  to  the  foreign 
particles  and  back  to  the  zinc  again. 

This  local  action  is  prevented  by  amalgamating  the  zinc. 
The  amalgam  brings  pure  zinc  to  the  surface,  covers  the 
foreign  particles,  and  above  all  forms  a  smooth  surface,  so 
that  a  film  of  hydrogen  clings  to  it  and  protects  it  from 
chemical  action  save  when  the  circuit  is  closed. 

449.  Polarization —  Connect  the  poles  of  a  voltaic  cell  to  a  gal- 
vanoscope and  note  the  deflection.  Let  the  cell  remain  in  circuit  with 
the  galvanoscope  for  some  time ;  the  deflection 
will  gradually  become  less  and  less.  Now  stir 
up  the  liquid  vigorously  with  a  glass  rod,  in- 
serting the  rod  between  the  plates  and  brush- 
ing off  the  adhering  gas  bubbles;  the  deflec- 
tion will  increase  nearly  to  its  first  value. 

Fasten  two  strips  of  zinc  and  two  of  copper 
to  a  square  board  and  immerse  them  in  dilute 
sulphuric  acid  (Fig.  383).  Join  one  zinc  and 
one  copper  strip  with  a  short  wire  for  a  few 
minutes.  Then  disconnect  and  join  the  two 
coppers  to  a  galvanoscope.  The  direction  of 
the  deflection  will  be  the  same  as  if  zinc  were 
used  in  place  of  the  copper  strip  coated  with 
hydrogen.  The  hydrogen-coated  copper  acts  like  zinc  and  tends  to 
produce  a  current  through  the  electrolyte  from  it  to  the  copper  free 
from  hydrogen. 

The  diminution  in  the  intensity  of  the  current  is  due  to 
several  causes,  but  the  chief  one  is  the  film  of  hydrogen 


FIGURE  383. -To  SHOW 
POLARIZATION. 


REMEDIES  FOR  POLARIZATION  369 

which  gathers  on  the  copper  plate,  causing  what  is  known 
as  the  polarization  of  the  cell.  The  hydrogen  on  the  posi- 
tive plate  not  only  introduces  more  resistance  to  the  flow  of 
the  current,  but  it  diminishes  the  electromotive  force  to 
which  this  flow  is  due.  The  presence  of  hydrogen  on 
the  copper  plate  sets  up  an  inverse  E.M.F.,  which  reduces 
the  flow. 

450.  Remedies  for  Polarization.  —  Place  enough  pure  mercury 
in  a  quart  jar  to  cover  the  bottom,  and  hang  above  it  a  piece  of  sheet 
zinc.  Fill  the  jar  with  a  nearly  saturated  solution  of  salt  water,  and 
place  in  the  mercury  the  exposed  end  of  a  copper  wire  insulated  with 
gutta-percha,  the  mercury  forming  the  positive  electrode  of  the  bat- 
tery. 

If  now  the  circuit  is  closed  through  a  telegraph  sounder  (§  552)  of 
ten  or  fifteen  ohms  resistance,  the  armature  will  at  first  be  attracted 
strongly ;  but  in  the  course  of  a  few  minutes  it  will  be  released  and 
will  be  drawn  back  by  the  spring.  Polarization  has  then  set  in  to  the 
extent  that  the  current  is  insufficient  to  operate  the  instrument. 

Next  take  a  small  piece  of  mercuric  chloride  (HgCl2)  no  larger 
than  the  head  of  a  pin,  and  drop  it  in  on  the  surface  of  the  mercury. 
The  armature  of  the  sounder  will  instantly  be  drawn  down,  showing 
that  the  current  has  recovered  its  normal  value.  The  hydrogen  has 
been  removed  by  the  chlorine  of  the  mercuric  chloride.  In  a  few 
minutes  the  chlorine  will  be  exhausted,  and  polarization  will  again 
set  in.  A  little  more  of  the  chloride  will  again  restore  the  activity  of 
the  cell.  (This  experiment  was  devised  several  years  ago  by  Mr.  D. 
H.  Fitch.) 

This  illustrates  a  chemical  method  of  reducing  polariza- 
tion. The  hydrogen  ions  are  replaced  by  others,  such  as 
copper  or  mercury,  which  do  not  produce  polarization 
when  they  are  deposited  on  the  positive  electrode ;  or  else 
the  positive  electrode  is  surrounded  with  a  chemical  which 
furnishes  oxygen  or  chlorine  to  unite  with  the  hydrogen 
before  it  reaches  the  electrode.  In  both  cases  the  elec- 
trode is  kept  nearly  free  from  hydrogen. 


870 


ELECTRIC  CURRENTS 


FIGURE  384.  —  DANIELL 
CELL. 


451.  The  Daniell  Cell.—  The  Daniell    cell  in   its   most 
common  form  (Pig.  381)  consists  of  a  glass  jar  containing 

a  saturated  solution  of  copper  sul- 
phate (CuSO4),  and  in  it  a  cylinder 
O  of  copper,  which  is  cleft  down  one 
side.  Within  the  copper  cylinder  is 
a  porous  cup  of  unglazed  earthenware 
containing  a  dilute  solution  of  zinc 
sulphate  (ZnSO4).  In  the  porous 
cup  also  is  the  zinc  prism  Z.  The 
copper  sulphate  must  not  be  allowed 
to  come  in  contact  with  the  zinc  elec- 
trode. The  porous  cup  allows  the 
ions  to  pass  through  its  pores,  but  it 
prevents  the  rapid  admixture  of  the 
two  sulphates. 
Both  electrolytes  undergo  partial  dissociation  into  ions ; 
and  when  the  circuit  is  closed,  the  zinc  and  the  copper 
ions  both  travel  toward  the  copper  electrode.  The  zinc 
ions  do  not  reach  the  copper,  because  zinc  in  copper  sul- 
phate replaces  copper,  forming  zinc  sulphate.  The  result 
is  the  formation  of  zinc  sulphate  at  the  zinc  electrode  and 
the  deposition  of  metallic  copper  on  the  copper  electrode. 
Polarization  is  completely  obviated ;  and,  so  long  as  the 
circuit  is  kept  closed,  the  mixing  of  the  electrolytes  by 
diffusion  is  slight.  This  cell  must  not  be  left  on  open 
circuit  because  the  copper  sulphate  then  diffuses  until  it 
reaches  the  zinc  and  causes  a  black  deposit  of  copper  oxide 
on  it. 

452.  The  Gravity  Cell.  —  This  cell  (Fig.  385)  is  a  modi- 
fied Daniell.     The  porous  cup  is  omitted^  and  the  partial 
separation  of  the  liquids  is  secured  by  difference  in  density. 
The  copper  electrode  O  is  placed  at  the  bottom  in  saturated 


THE  DRY  CELL 


371 


copper  sulphate  .5,  while  the  zinc  Z  is  suspended  near  the 
top  in  a  weak  solution  of  zinc  sulphate  A,  floating  on  top 
of  the  copper  sulphate.  The  zinc 
should  never  be  placed  in  the  solution 
of  copper  sulphate.  The  saturated 
copper  sulphate  is  more  dense  than 
the  dilute  zinc  salt,  and  so  remains 
at  the  bottom,  except  as  it  slowly  dif- 
fuses upward. 

453.  The  Leclanche  Cell  consists  of  a 
glass   vessel   containing  a  saturated 
solution  of  ammonium  chloride  (sal 

ammoninc)  in  which  stands  a  zinc  FIGURE  385.—  THE  GRAV- 
rod  and  a  porous  cup  (Fig.  386). 

In  this  porous  cup  is  a  bar  of  carbon  very  tightly  packed 
in  a  mixture  of  manganese  dioxide  and  graphite,  or  granu- 
lated carbon. 

The  zinc  is  acted  on  by  the  chlorine  of  the  ammonium 
chloride,  liberating  ammonia  and  hydrogen.  The  am- 
monia in  part  dissolves  in  the  liquid, 
and  in  part  escapes  into  the  air.  The 
hydrogen  is  slowly  oxidized  by  the 
manganese  dioxide.  The  cell  is  not 
adapted  to  continuous  use,  as  the  hy- 
drogen is  liberated  at  the  positive 
electrode  faster,  than  the  oxidation 
goes  on,  arid  hence  the  cell  polarizes. 
If,  however,  it  is  allowed  to  rest,  it  re- 
covers from  polarization.  The  Le- 
clanche' cell  is  suitable  for  ringing 
electric  bells. 

454.  The  Dry  Cell.  —  The  "  dry  "  cell  is  merely  a  modi- 
fied   Leclanche   specially  adapted   for   use   in   situations 


FIGURE  386. —THE  LE- 
CLANCHE CELL. 


372 


ELECTRIC   CURRENTS 


where  cells  with  a  liquid  electrolyte  cannot  be  used. 
The  electrodes  are  zinc  and  carbon.  The  cylindrical  zinc 
pot  Z  (Fig.  387)  is  contained  in  a  cardboard  case.  It  is 
lined  with  porous  pulp  board,  which  serves  the  double 
purpose  of  taking  up  part  of  the  liquid  content  of  the  cell 

and  separating  the  solid  part  from 
the  zinc.  The  carbon  is  either 
round  or  flat  (shown  edgeways  in 
the  figure).  Between  the  two 
electrodes  is  a  moist  paste  or 
"  mix  "  of  varied  composition,  but 
containing  the  essential  sal  am- 
moniac, besides  granulated  car- 
bon, graphite,  zinc  chloride,  and 
manganese  dioxide.  The  cell  is 
sealed  with  wax  or  pitch. 

Dry  cells  of  the  standard  size, 
2|  x  6  inches,  are  now  made  that 
yield  a  •  current  of  25  to  30  am- 
peres (§  469)  on  short  circuit. 
Smaller  sizes  in  great  numbers  are 
used  to  light  miniature  electric  lights  in  hand  lamps  or 
flash  lights.  Some  fifty  millions  of  "  standard  "  dry  cells 
are  now  manufactured  yearly  in  the  United  States,  and 
probably  several  times  that  number  of  small  cells  for  hand 
lamps.  In  addition  to  their  application  in  flash  lights, 
dry  cells  are  much  used  for  ringing  bells,  running  clocks, 
and  working  spark  coils  for  ignition  in  gas  engines  on 
boats  and  automobiles.  It  should  not  be  forgotten  that 
dry  cells  must  not  be  left  on  closed  circuit. 

455.  The  Lalande  Cell.  —  The  negative  is  zinc  and  the 
exciting  liquid  is  a  30  per  cent  solution  of  caustic  potash. 
The  zinc  dissolves  in  the  alkali,  forming  zincate  of  potas- 


FIGURE  387.  —  DRY  CELL. 


ELECTROLYSIS   OF  COPPER   SULPHATE  373 

slum  and  setting  free  hydrogen.  The  positive  electrode 
is  a  compressed  cake  of  copper  oxide,  held  in  a  copper 
frame.  The  hydrogen  reduces  the  copper  oxide  to  me- 
tallic copper.  The  exciting  liquid  must  be  covered  with 
oil  to  exclude  the  carbonic  acid  gas  of  the  air,  which 
converts  the  alkali  into  a  carbonate.  This  cell  has  an 
electromotive  force  but  little  more  than  half  that  of  the 
Leclanche*,  but  it  is  capable  of  furnishing  a  large  and 
constant  current.  On  this  account  it  is  much  used  to 
work  railway  signals. 

II.   ELECTROLYSIS 

456.  Phenomena    of    Electrolysis.  —  Thrust   platinum   wires 
through  the  corks  closing  the  ends  of  a  V-tube  (Fig.  388).     Fill  the 
tube  nearly  full  with   a  solution  of 

sodium    sulphate    colored    with   blue* 

litmus.     Pass  through  it  a  current  for 

a  few   minutes.     The   liquid  around 

the  anode,   where  the  current  enters, 

will  turn  red,  showing  the  formation 

of  an  acid;    the   liquid  around  the 

cathode,  where  the  current  leaves  the 

cell,  will  turn  a  darker  blue,  showing         FIGURE  388.  — V-TUBE  FOR 

the  presence  of  an  alkali.  ELECTROLYSIS. 

The  electric  current  in  its  passage  through  a  liquid 
decomposes  it.  This  process  of  decomposing  a  liquid  by 
an  electric  current  Faraday  named  electrolysis;  the  liquid 
decomposed  he  called  the  electrolyte;  the  parts  of  the 
separated  electrolyte,  ions.  The  current  enters  the  elec- 
trolyte by  the  anode  (meaning  the  way  in)  and  leaves  it  by 
the  cathode  (meaning  the  way  out). 

457.  Electrolysis  of  Copper  Sulphate.  —  Fill  the  V-tube  of  the 
last  experiment  about  two-thirds  full  of  a  solution  of  copper  sulphate. 
•.After  the  circuit  has  been  closed  a  few  minutes,  the  cathode  will  be 


374 


ELECTRIC  CURRENTS 


covered  with  a  deposit  of  copper,  and  bubbles  of  gas  will  rise  from 
the  anode.  These  bubbles  are  oxygen. 

When  copper  sulphate  is  dissolved  in  water  it  is  dis- 
sociated to  some  extent.     If,  therefore,  electric  pressure 

is   applied  to  the   solution   through   the   electrodes,    the 

++ 
electropositive  ions  (Cu)  are  set  moving  from  higher  to 

lower  potential,  while  the  electronegative  ions  (SO4)  carry 

their  negative  charges  in  the  opposite  direction.  The  Cu 
ions  are  therefore  driven  against  the  cathode,  and,  giving 
up  their  charges,  become  metallic  copper.  The  sulphions 

(SO4)  go  to  the  anode ;  and,  giving  up  their  charges, 
they  take  hydrogen  from  the  water 
present,  forming  sulphuric  acid 
(H2SO4)  and  setting  free  oxygen, 
which  comes  off  as  bubbles  of  gas.  If 
the  anode  were  copper  instead  of  plati- 
num, the  sulphion  would  unite  with  it, 
forming  copper  sulphate,  and  copper 
would  be  removed  from  the  anode  as 
fast  as  it  is  deposited  on  the  cathode. 
The  result  of  the  passage  of  a  current 
would  then  be  the  transfer  of  copper 
from  the  anode  to  the  cathode.  This 
is  what  takes  place  in  the  electrolytic 
refining  of  copper. 

Thus  the  passage  of  an  electric  cur- 
rent through  an  electrolyte  is  accom- 
plished in  the  same  way,  whether  it  is 
in  a  voltaic  cell  or  in  an  electrolytic 
cell. 
458.  Electrolysis  of  Water.  — Water  appears  to  have  been 

the  first  substance  decomposed  by  an  electric  current.     Pure. 


FIGURE  389.  — HOF- 
MANN'S  APPARATUS  FOR 
ELECTROLYSIS  OF 
WATER. 


LAWS   OF  ELECTROLYSIS  375 

water  does  not  conduct  an  appreciable  current  of  elec- 
tricity, but  if  it  is  acidulated  with  a  small  quantity  of 
sulphuric  acid,  electrolysis  takes  place. 

In  Hofmann's  apparatus  (Fig.  389)  the  acidulated  water  is  poured 
into  the  bulb  at  the  top,  and  the  air  escapes  by  the  glass  taps  until 
the  tubes  are  filled.  The  electrodes  at  the  bottom  in  the  liquid  are 
platinum  foil.  If  a  current  is  sent  through  the  liquid,  bubbles  of  gas 
will  be  liberated  on  the  pieces  of  platinum  foil.  The  gases  collecting 
in  the  tubes  may  be  examined  by  letting  them  escape  through  the 
taps.  Oxygen  will  be  found  at  the  anode  and  hydrogen  at  the 
cathode  ;  the  volume  of  the  hydrogen  will  be  nearly  twice  that  of  the 
oxygen. 

459.  Laws  of  Electrolysis.  —  The  following  laws  of  elec- 
trolysis were  established  by  Faraday. 

I.  The  mass  of  an  electrolyte  decomposed  by  an  electric 
current  is  proportional  to  the  quantity  of  electricity  con- 
veyed through  it. 

The  mass  of  an  ion  liberated  in  one  second  is,  therefore, 
proportional  to  the  strength  of  current. 

II.  When  the  same  quantity  of  electricity  is  conveyed 
through  different  electrolytes,  the  masses  of  the  different 
ions  set  free  at  the  electrodes  are  proportional  to  their 
chemical  equivalents. 

By  "  chemical  equivalents "  are  meant  the  relative 
quantities  of  the  ions  which  are  chemically  equivalent  to 
one  another,  or  take  part  in  equivalent  chemical  reactions. 
Thus,  32.5  g.  of  zinc  or  31.7  g.  of  copper  take  the  place  of 
one  g.  of  hydrogen  in  sulphuric  acid  (H2SO4)  to  form  zinc 
sulphate  (ZnSO4)  or  copper  sulphate  (CuSO4),  respec- 
tively. 

The  first  law  of  electrolysis  affords  a  valuable  means  of 
comparing  the  strength  of  two  electric  currents  by  deter- 


876  ELECT 'HIC   CURRENTS 

mining  the  relative  masses  of  any  ion,  such  as  silver  or 
copper,  deposited  by  the  two  currents  in  succession  in  the 
same  time  (§  469). 

460.  Electroplating  consists  in  covering   bodies  with  a 
coating  of  any  metal  by  means  of  the  electric  current. 
The  process  may  be  summarized  as  follows:    Thoroughly 
clean  the  surface  to  remove  all  fatty  matter.     Attach  the 
article  to  the  negative  electrode  of   a  battery,  and   sus- 
pend it  in  a  solution  of  some  chemical  salt  of  the  metal 
to  be    deposited.     If  silver,   cyanide  of   silver  dissolved 
in  cyanide  of  potassium  is  used;   if  copper,  sulphate  of 
copper.     To  maintain  the  strength  of  the  solution  a  piece 
of   the   metal   of   the  kind   to   be    deposited  is   attached 
to  the  positive  electrode  of  the  battery  and  immersed  in 
the  electrolyte.     The  action  is  similar  to  that  heretofore 
given.     Articles  of  iron,  steel,  zinc,  tin,  and  lead  cannot 
be  silvered  or  gilded  unless  first  covered  with  a  thin  coat- 
ing of  copper. 

All  silver  plating,  nickeling,  gold  plating,  and  so  on,  is 
done  by  this  process. 

461.  Electrotyping  consists  in  copying  medals,  wood-cuts, 
type,  and  the  like  in  metal,  usually  copper,  by  means  of  the 
electric  current.     A  mold  of  the  object  is  taken  in  wax  or 
plaster  of  Paris.     This  is  evenly  covered  with  powdered 
graphite  to  make  the  surface  a  conductor,  and  treated  very 
much  as  an  object  to  be  plated.     When  the  deposit  has  be- 
come sufficiently  thick  it  is  removed  from  the  mold  and 
backed  or  filled  with  type-metal. 

Nearly  all  books  nowadays  are  printed  from  electrotype 
plates,  and  not  as  formerly  from  movable  types. 

462.  The  Storage  Cell.  —  Attach  two  lead  plates,  to  which  are 
soldered  copper  wires,  to  the  opposite  sides  of  a  block  of  dry  wood, 
and  immerse  them  in  dilute  sulphuric  acid,  one  part  acid  to  five  of 


THE  STORAGE  CELL 


377 


water  (Fig.  390).  Connect  this  cell  to  a  suitable  battery  B  by  means 
of  key  KI  ;  also  to  an  ordinary  electric  house  bell  H  through  a  key  K2 
(Fig.  391).  A  galvanoscope  G  may  be  included  in  the  circuit  to  show 
the  direction  of  the  current.  Pass  a  cur- 
rent through  the  lead  cell  for  a  few  min- 
utes by  closing  the  key  Kv  Hydrogen 
bubbles  will  be  disengaged  from  the 
cathode,  while  the  anode  will  begin  to 
turn  dark  brown.  Next  open  the  key 
Kv  thus  disconnecting  the  battery  B,  and 
close  key  K2.  The  bell  will  ring  and  the 
galvanoscope  will  indicate  a  discharge 
current  in  the  opposite  direction  to  the 
first  or  charging  current.  The  bell  will 
soon  cease  ringing,  and  the  charging  may 

be  repeated  by  again  closing  key  K,  while 

„.  FIGURE  390.  — SIMPLE  STOR- 

*2  is  open.  AGE  CELL. 

The  lead  plates  in  an  electrolyte  of  sulphuric  acids  il- 
lustrate a  simple  lead  storage  cell.  The  electrolysis  of  the 
sulphuric  acid  liberates  oxygen  at  the  anode,  which  com- 
bines with  the  lead  electrode  to  form  a  chocolate-colored 
deposit  of  lead  peroxide  (PbO2).  Hydrogen  accumulates 

on  the  cathode.  When  the 
charging  battery  is  discon- 
nected and  the  lead  plates  are 
joined  by  a  conductor,  a  cur- 
rent flows  in  the  external 
circuit  from  the  chocolate - 
colored  plate,  which  is  called 
the  positive  electrode,  to  the 
other  one,  called  the  negative;  the  lead  peroxide  is 
reduced  to  spongy  lead  on  the  positive  plate,  while  some 
lead  sulphate  is  formed  on  the  negative.  During 
subsequent  charging  this  lead  sulphate  is  reduced  by 
the  hydrogen  to  spongy  lead.  Note  that  the  charging 


4u 

"-©— MI 

<?  B 


FIGURE  391.  —  CHARGING  AND  DIS- 
CHARGING STORAGE  CELL. 


378 


ELECTRIC   CURRENTS 


current  passes  through  the  storage  cell  in  the  opposite 
direction  to  the  discharge  current  furnished  by  the  cell 
itself. 

The  storage  battery  stores  energy  and  not  electricity.  The 
energy  of  the  charging  current  is  converted  into  the  poten- 
tial energy  of  chemical  separation  in 
the  storage  cell.  When  the  circuit  of 
the  charged  secondary  cell  is  closed, 
the  potential  chemical  energy  is  re- 
converted into  the  energy  of  an  electric 
current  in  precisely  the  same  way  as  in 
a  primary  cell. 

Figure  392  shows  a  complete  storage 
cell  containing  one  positive  and  two 
negative  plates. 

463.  The  Edison  Storage  Cell.  —  The 
positive  electrode  of  this  cell  consists 
of  hydrated  nickel  oxide  packed  in  a 
steel  grid;  the  negative,  of  finely  di- 
vided iron  packed  in  another  grid. 
The  electrolyte  is  a  solution  of  caustic  potash.  During 
the  discharge  the  iron  is  oxidized  and  the  nickel  oxide  is 
reduced.  These  cells  are  lighter  and  stronger  than  lead 
storage  cells  and  they  may  be  charged  more  rapidly;  but 
their  E.M.F.  is  lower  and  their  efficiency  less. 

III.    OHM'S  LAW  AND   ITS   APPLICATIONS 

464.  Resistance.  —  Every  conductor  presents  some  ob- 
struction to  the  passage  of  electricity.  This  obstruction 
is  called  its  electrical  resistance.  The  greater  the  con- 
ductance of  a  conductor  the  less  its  resistance,  the  one 
decreasing  in  the  same  ratio  as  the  other  increases. 
Resistance  is  the  reciprocal  of  conductance.  If  R  is  the 


FIGURE  392.  —  STOR- 
AGE CELL  WITH  THREE 
PLATES. 


EFFECT  OF  HEAT  ON   RESISTANCE  379 

resistance  of   a  conductor  and   0  its  conductance,  then 


465.  Unit  of  Resistance.  —  The  primary  standard  unit  of 
resistance  is  the  ohm.     It  is  represented  by  the  resistance 
of  a  uniform  thread  of  mercury  106.3  cm.  long  and  14.5421 
g,  in  mass,  at  0°  C.     This  standard  is  reproducible  because 
mercury  can  be  obtained  in  great  purity. 

A  commercial  standard  for  practical  purposes  consists 
of  a  resistance  coil  of  suitable  wire,  adjusted  to  be  exactly 
equal  to  the  primary  legal  mercury  standard  at  some 
definite  temperature. 

466.  Laws  of  Resistance.  —  1.  The  resistance  of  a  con- 
ductor is  proportional  to  its  length.     For  example,  if  39  ft. 
of  No.  24  copper  wire  (B.  &-S.  gauge}  have  a  resistance 
of  1  ohm,  then  78  ft.  of  the  same  wire  will  have  a  resist- 
ance of  2  ohms. 

2.  The  resistance  of  a  conductor  is  inversely  propor- 
tional to  its  cross  sectional  area.     In  the  case  of  round  wire 
the  resistance  is  therefore  inversely  proportional  to  the 
square  of  the  diameter.     For  example,  No.  24  copper  wire 
has  twice  the  diameter  of  No.  30.     Then  39  ft.  of  No.  24  has 
a  resistance  of  1  ohm,  and  9.75  ft.  of  No.  30  (one-fourth 
of  39)  also  has  a  resistance  of  1  ohm,  both  at  22°  C. 

3.  The  resistance  of  a  conductor  of  given  length  and 
cross  section  depends  upon  the  material  of  which  it  is 
made,  that  is,  upon  the  specific  resistance,  or  resistivity  of 
the  material.     For  example,  the  resistance  of  2.  2  ft.  of  No. 
24  German  silver  wire  is  1  ohm,  while  it  takes  .39  ft.  of  cop- 
per wire  of  the  same  diameter  to  give  the  same  resistance. 

467.  Effect  of  Heat  on  Resistance.  —  Changes  of  tempera- 
ture affect  temporarily  the  resistance  of  metals,  but  all 
metals  are  not  affected  to  the  same  extent.     Nearly  all 


380  ELECTRIC  CURRENTS 

pure  metals  show  an  increase  in  resistance  of  about  0.4 
per  cent  for  a  rise  of  temperature  of  1°  C.,  or  40  per  cent 
for  100°. 

When  metals  are  cooled  in  liquid  air,  their  resistance 
falls  greatly.  The  experiments  of  Dewar  and  Fleming 
show  that  the  decrease  in  resistance  of  all  pure  metals  is 
such  that  at  the  absolute  zero,  —  273°  C.,  they  tend  to 
become  perfect  conductors.  Recently  Kameiiingh  Onnes 
has  found  that  in  liquid  helium,  —  269°  C.,  tin  and  lead 
lose  all  appreciable  resistance  and  become  what  he  calls 
super-conductors.  A  current  started  by  induction  in  a 
closed  coil  of  lead  wire  continued  almost  undiminished  for 
several  hours  without  any  electromotive  force.  It  con- 
tinued to  flow  as  if  by  its  inertia  without  encountering 
resistance. 

The  resistance  temperature  coefficient  of  alloys  is  smaller 
than  that  of  pure  metals.  That  of  German  silver  is  only 
0.00044  for  1°  C.,  that  is,  one-tenth  that  of  the  pure  metals. 
Such  alloys  as  manganin  and  cqnstantan  have  practically 
no  temperature  coefficient.  This  property  makes  them 
very  useful  for  resistance  coils. 

The  resistance  of  carbon  and  of  electrolytes,  unlike  that 
of  metals,  falls  on  heating.  The  resistance  of  the  filament 
of  a  carbon  incandescent  lamp  (16  candle  power),  which 
is  some  400  ohms  when  cold,  is  only  220  ohms  when  white 
hot. 

468.  Formula  for  Resistance.  —  The  above  laws  are  con- 
veniently expressed  in  the  following  formula  for  the  re- 
sistance of  a  wire : 


iii  which  k  is  a  constant  depending  on  the  material,  I  the 
length  of  the  wire  in  feet,,  and    C.M.  denotes  "circular 


ELECTROMOTIVE  FORCE  381 

mils."  A  umil"  is  a  thousandth  of  an  inch,  and  circular 
mils  are  the  square  of  the  mils  ;  that  is,  the  square  of  the 
diameter  of  the  wire  in  thousandths  of  an  inch.  For  ex- 
ample, if  the  diameter  of  a  wire  is  0.020  in.,  then  in  mils  it 
is  20,  and  the  circular  mils  (C.M.)  will  be  the  square  of 
20  or  400.  Now  if  the  length  of  a  wire  conductor  is  ex- 
pressed in  feet  and  its  cross  section  in  circular  mils,  then 
it  is  easy  to  give  to  k  for  each  kind  of  conductor  such  a 
value  that  R  in  the  above  formula  will  be  in  ohms.  ' 

The  following  are  the  values  of  k  in  ohms  for  several 
metals,  at  20°  C.: 

Silver        9.53        Iron  61.3    •    German  silver   181.3 

Copper   10.19        Platinum   70.5        Mercury  574.0 

469.  Strength  of  Current.  —  The  strength  or  intensity  of 
a  current  is  measured  by  the  magnitude  of  the  effects  pro- 
duced by  it.     Any  such  effect  may  be  made  the  basis  of  a 
system  of  measurement.     The  quantity  of  an  ion  deposited 
in  a  second  is  a  convenient  one  to  use  in  defining  unit 
strength  of  current.     The  unit  of  current  strength  is  the 
ampere.     It  is  defined  as  the  current  which  will  deposit  by 
electrolysis,  under  suitable  conditions,  0.001118  g.  of  silver 
per  second.     The  ampere  deposits  4.025  g.  of  silver  in  one 
hour.     A  milliampere  is  a  thousandth  of  an  ampere.     It  is 
to  be  noted  that  the  electrolytic  method  measures  only  the 
quantity  of  electricity  passing  through  the  decomposing 
cell,  called  a  voltameter,  or  a  coulometer,  in  the  given  time. 

470.  Electromotive  Force  is  the  cause  of  an  electric  flow. 
It  is  often  called  electric  pressure  from  its  superficial  anal- 
ogy to  water  pressure.     The  unit  of  electromotive  force 
(E.M.F.)  is  the  volt.     A  volt  is  the  E.M.F.  which  will  cause 
a  current  of  one  ampere  to  flow  through  a  resistance  of  one 
ohm.     The  E.M.F.  of  a  voltaic  cell  depends  upon  the  ma- 


382 


ELECTRIC  CURRENTS 


Cadmium  sulphate  _ 
crystals  and  solution 


terials  employed,  and  is  entirely  independent  of  the  size 
and  shape  of  the  plates.  The  E.M.F.  of  a  Daniell  cell 
and  of  a  gravity  cell  is  about  1.1  volts;  of  a  Leclanchej 
and  of  a  dry  cell,  1.5  volts  ;  of  a  lead  storage  cell,  2  volts. 
The  practical  international  standard  of  electromotive 
force  is  the  Weston  Normal  Cell.  The  electrodes  are  cad- 

mium amalgam  for 
the  negative  and 
mercury  for  the 
positive.  The  elec- 
trolyte is  a  satu- 
rated solution  of 
cadmium  sulphate, 
and  the  depolarizer 
is  mercurous  sul- 
phate (Fig.  893).  The  E.M.F.  of  the  Weston  cell  in 
volts  is  given  by  the  following  equation,  the  temperature 
t  being  in  centigrade  degrees  : 

E=  1.0183  -  0.00004  (t  -  20°).     (Equation  35) 

471.  Ohm's  Law.  —  The  definite  relation  existing  be- 
tween strength  of  current,  resistance,  and  E.M.F.  is 
known  as  Ohm's  Law  : 

The  strength  of  a  current  equals  the  electromotive  force 
divided  by  the  resistance;  then 


Cadmium 


Mercurous  sulphate 
paste 

Platinum  wiret 
Mercury 

FIGURE  393.  —  WESTON  NORMAL  CELL. 


current  in  amperes 
or  in  symbols, 


EMJf-  ^  P°tential  difference-)  in  volts 


resistance  in  ohms 


. 

R 


(Equation  36) 


where  I  is  the  current  in  amperes,  E  the  E.M.F.  in  volts, 
and  R  the  resistance  in  ohms.     Applied  to  a  battery,  if 


Alessandro  Volta  (1745- 
1827)  was  born  at  Como,  It- 
aly. He  was  professor  of 
physics  at  the  University  of 
Pavia,  and  was  noted  for  his 
researches  and  investigations 
in  electricity.  The  voltaic 
cell,  the  electroscope,  the 
electrical  condenser,  and  the 
electrophorus  are  due  to  his 
genius. 


Georg  Simon  Ohm  ( 1 789- 
1854)  was  born  in  Erlangen, 
Bavaria,  and  was  educated 
at  the  University  of  that 
town.  He  began  his  inves- 
tigations by  measuring  the 
electrical  conductivity  of 
metals.  In  1827  he  an- 
nounced the  electrical  law 
named  in  his  honor,  and  in 
1842  he  was  elected  to  a  pro- 
fessorship in  the  University 
of  Munich: 


CONNECTING  IN   SERIES 


r  is  the  resistance  external  to  the  cell,  and  r'  the  internal 
resistance  of  the  cell  itself,  then 


J= 


u 

r+r' 


(Equation  37) 


From  Equation  36,  E '  =  IR  and  R  =  -- 

472.  Methods  of  Varying  Strength  of  Current.  —  It  is  evi- 
dent  from   Ohm's  law  that  the  strength  of  the  current 
furnished  by  an  electric  generator  may  be  increased  in 
two  ways:  (1)  by  increasing  the  E.M.F.;  (2)  by  reducing 
the  internal  resistance. 

The  E.M.F.  may  be  increased  by  joining  several  cells 
in  series^  and  the  internal  resistance  may  be  diminished  by 
connecting  them  in  parallel. 
Enlarging  the  plates  of  a  bat- 
tery or  bringing  them  closer 
together  diminishes  the  in- 
ternal resistance. 

473.  Connecting  in  Series.  — 
To  connect  cells  in  series,  join 
the  positive  electrode  of  one 
to  the   negative  electrode  of 
the  next,  and  so  on  until  all 
are  connected.    The  electrodes 

of  the  battery  thus  connected  in  series  are  the  positive 

electrode  of  the  last  one  in  the  series 

_  .1      and  theriegative  electrode  of  the  first 

xn    I     J2JL^        one  (F*£*  394).     Figure  395  is  the 

conventional  sign  for  a  single  cell ; 

Figure  396  shows  four  cells  in  series. 

Pt_.  ._  on,-      ~ ,,  When  n  similar  cells  are  connected 

FIGURE  OVO.  —  blGN  FOR 

SINGLE  CELL.  in  series,  the  E.M.i .  of  the  battery  is 


FIGURE  394.  —  CELLS  CONNECTED 
IN  SERIES. 


384 


ELECTRIC   CURRENTS 


n  times  that  of  a  single  cell;  the  resistance  is  also  n  times 
the  resistance  of  one  cell.     Hence,  by  Ohm's  law  for  n 

cells  connected  in  series  the 

current  is 

1= 


FIGURE  396.  —  FOUR  CELLS 
SERIES. 


nrr 

To  illustrate,  if  four  cells, 
each  having  E.M.F.  of  2  volts 
and  an  internal  resistance  of 
0.5  ohm,  are  joined  in  series 
with  an  external  resistance  of  10  ohms,  the  current  will  be 

1= =  0.67  ampere. 

10  +  4x0.5 

474.  Connecting  in  Parallel.  —  When  all  the  positive  ter- 
minals are  connected  together  on  one  side  and  the 
negative  on  the  other,  the 
cells  are  grouped  in  parallel 
(Fig.  397).  With  n  similar 
cells  the  effect  of  such  a 
grouping  is  to  reduce  the  in- 
ternal resistance  to  -th  that 
n 

of  a  single  cell.  It  is  equiv- 
alent to  increasing  the  area 
of  the  plates  n  times.  All  the  cells  side  by  side  contribute 
equal  shares  to  the  output  of  the  battery.  The  E.M.F. 
of  the  group  is  the  same  as  that  of  a  single  cell. 

Connection  in  parallel  is  used  chiefly  with  storage  cells,  not  for  the 
purpose  of  reducing  the  internal  resistance  of  the  battery,  but  for  the 
purpose  of  permitting  a  larger  current  to  be  drawn  from  it  with  safety 
to  the  cells.  The  ampere  capacity  of  a  storage  cell  depends  on  the  area 
of  the  plates.  If  twenty  amperes  may  be  drawn  from  a  single  storage 
cell,  then  from  two  such  cells  in  parallel  forty  amperes  may  be  taken. 


FIGURE  397.  —  CELLS  IN  PARALLEL. 


JOULE'S  LAW  885 

IV.  HEATING.  EFFECTS  OF  A  CURRENT 

475.  Electric  Energy  Converted  into  Heat.  —  Send  an  electric 
current  through  a  piece  of  fine  iron  wire.     The  wire  is  heated,  and  it 
may  be  fused  if  the  current  is  sufficiently  strong. 

The  conversion  of  electrical  energy  into  other  forms  is 
a  familiar  fact.  In  the  storage  battery  the  energy  of  the 
charging  current  is  converted  into  the  energy  of  chemical 
separation  and  stored  as  the  potential  energy  of  the 
charged  cells.  In  this  experiment  the  energy  of  the  cur- 
rent is  transformed  into  heat  because  of  the  resistance 
which  the  wire  offers.  If  the  resistance  of  an  electric 
circuit  is  not  uniform,  the  most  heat  will  be  generated 
where  the  resistance  is  the  greatest. 

Send  the  current  from  a  few  cells  through  a  chain  made  of  alter- 
nate pieces  of  iron  and  copper,  soldered  together  (iig.  398).  The 
iron  links  may  be  made  to  _ — «^c  r 

glow  red  hot,  while  the  copper  ^^"'^'^^^C        I  ^S^'''^ 

ones    remain    comparatively 

._.  .  .  .    ,.J       FIGURE  398.  —  IRON  AND  COPPER  LINKS. 

cool.     Ihe  resistance  ot   the 

iron  wire  is  about  seven  times  as  great  as  that  of  copper  of  the  same 
length  and  gauge.  Moreover,  its  thermal  capacity  is  about  three- 
quarters  as  great.  Hence  the  rise  of  temperature  of  the  iron  links  is 
roughly  nine  times  as  great  as  that  of  the  copper  ones. 

476.  Joule's  Law.  —  Joule  demonstrated  experimentally 
that  the  number  of  units  of  heat  generated  in  a  conductor 
by  an  electric  current  is  proportional: 

a.  To  the  resistance  of  the  conductor. 

b.  To  the  square  of  the  strength  of  current. 

c.  To  the  length  of  time  the  current  flows.1 


1  If  H  is  the  heat  in  calories,  I  the  current  strength  in  amperes,  E  the 
resistance  in  ohins,  t  the  time  in  seconds,  and  0.24  the  number  of  calories 
equivalent  to  one  joule,  then  the  heat  equivalent  of  a  current  is 
H=  0.24  x  I*m  calories. 


386 


ELECTRIC  CURRENTS 


FIGURE  399.  —  CARTRIDGE  FUSE. 


477.  Applications  of  Electric  Heating.  —  Some  of  the  more 
important  applications  of  electric  heating  are  the  following  : 

1.  Electric  Cautery.     A  thin  plati- 
num wire  heated  to  incandescence  is 
employed  in  surgery  instead  of  a  knife. 
Platinum  is  very  infusible  and  is  not 
corrosive. 

2.  Safety  Fuses.  Advantage  is  taken 
of  the  low  temperature  of  fusion  of  some  alloys,  in  which  lead  is  a 
constituent,  for  making  safety  fuses  to  open  a  circuit  automatically 
whenever  the  current  becomes  excessive  (Fig. 

399). 

3.  Electric  Welding.     If  the  abutting  ends 
of  two  rods  or  bars  are  pressed  together,  while 
a  large  current  passes   through  them,  enough 
heat  is  generated  at  the  junction,  where  the  re- 
sistance is  greatest,  to  soften  and  weld  them  to- 
gether.    Figure  400  shows  two  welded  joints  as 
they  came  from  the  welder. 

4.  The  Electric  Flatiron.     Figure  401  shows 
a  flatiron,  partly  cut   away,   arranged   to   be 
heated  by  an  electric  current.     The   current 
enters  by  a  flexible  conductor  and  flows  through 
the  resistance  coil  E  on  the  base  of  the  iron. 

A  is  a  wooden  handle  to  avoid  the  use  of  a  holder. 


FIGURE  400.  —  ELEC- 
TRICALLY  WELDED 

JOINTS. 


The  resistance 

is  often  arranged  so  as  to  con- 
centrate the  heat  at  the  point 
of  iron. 

5.  Electric  Heating.  Electric 
street  cars  are  often  heated  by  a 
current  through  suitable  resist- 
ances. Similar  devices  for  cook- 
ing are  now  articles  of  com- 
merce. Small  furnaces  for  fus- 
ing, vulcanizing,  and  enameling 
are  common  in  dentistry. 
FIGURE  40 1 .—  ELECTRIC  FLATIRON.  Large  furnaces  are  employed 

for  melting  refractory  substances,  for  the .  reduction  of  certain  ores, 
and  for  chemical  operations  demanding  a  high  temperature. 


MAPPING   THE  MAGNETIC  FIELD 


387 


V.   MAGNETIC  PROPERTIES  OF  A  CURRENT 

478.  Magnetic  Field  Around  a  Conductor.  —  Dip  a  portion  of 
a  wire  carrying  a  heavy  current  into  fine  iron  filings.  A  thick  cluster 
of  them  will  adhere  to  the 
wire  (Fig.  402) ;  they  will 
drop  off  as  soon  as  the  cir-  FIGURE  402.  —  MAGNETIC  FIELD  AROUND  A 
cuit  is  opened.  CURRENT. 

The  experiment  shows  that  a  conductor  through  which 
an  electric  current  is  passing  has  mag- 
netic properties.  The  iron  filings  are 
magnetized  by  the  current  and  set 
themselves  at  right  angles  to  the  wire. 
When  the  circuit  is  broken,  they  lose 
their  magnetism  and  drop  off. 

479.   Mapping  the  Magnetic  Field.  — 

Support  horizontally  a  sheet  of  cardboard  or 
of  glass  LB  with  a  hole  through  it.  Pass 
vertically  through  the  hole  a  wire,  W,  con- 
necting with  a  suitable  electric  generator,  so 
that  a  strong  current  can  be  sent  through 
the  circuit  (Fig.  403).  Close  the  circuit  and 

sift  iron  filings  on  the  paper  or  glass  about  the  wire,  jarring  the  sheet 

by  tapping  it.  The  filings  will  ar- 
range themselves  in  circular  lines 

about    the     wire.     Place     a    small 

mounted    magnetic    needle    on    the 

sheet  near  the  wire ;  it  will  set  itself 

tangent  to  the  circular  lines,  and  if 

the  current  is  flowing  downward,  the 

north  pole  will  point  in  the  direction 

in  which  the  hands  of  a  watch  move. 

The  lines  of  magnetic  force 
about  a  wire  through  which  an 

electric  current  is  flowing,  are     FIQURE  4Q4  _  CIRCULAR  LmEg  op 
concentric  circles.     Figure  404  FORCE  AROUND  A  WIRE. 


w 


FIGURE  403.  —  MAPPING 
MAGNETIC  FIELD. 


388 


ELECTRIC  CURRENTS 


was  made  from  a  photograph  of  these  circular  lines  of  force 
as  shown  by  iron  filings  on  a  plate  of  glass.  Their  direc- 
tion relative  to  the  current 
is  given  by  the  following 
rule: 


Crrasp  the  wire  by  the  right 
hand  so  that  the  extended  thumb 
points    in    the    direction    of 
FIGURE  405.  —  FINGERS  SHOW DIREC-    the  current;    then  the  fingers 
TION  OF  LINES  OF  FORCE.  wrapped  around  the  wire  indi- 

cate the  direction  of  the  lines  of  force  (Fig.  405). 

Figure  406  is  a  sketch  intended  to  show  the  direction  of 


FIGURE  406.  —  MAGNETIC  WHIRL. 

these  circular  lines  of  magnetic  force  (or  magnetic  whirl) 
which  everywhere  surround  a  wJ»re  conveying  a  current. 

480.  Properties  of  a  Circular  Con- 
ductor. —  Bend  a  copper  wire  into  the  form 
shown  in  Figure  407,  the  diameter  of  the  cir- 
cle being  about  20  cm.  Suspend  it  by  a  long 
untwisted  thread,  so  that  the  ends  dip  into 
the  mercury  cups  shown  in  cross  section  in 
the  lower  part  of  the  figure.  Send  a  cur- 
rent through  the  suspended  wire  by  connect- 
ing a  battery  to  the  binding  posts.  A  bar 
magnet  brought  near  the  face  of  the  circular 
conductor  will  cause  the  latter  to  turn  about 
a  vertical  axis  and  take  up  a  position  with 
its  plane  at  right  angles  to  the  axis  of  the 

magnet.     With  a  strong  current  the  circle         FIGURE  407  DEFLEC- 

will  turn  under  the  influence  of  the  earth's     TION    OF   CIRCULAR   CUR- 
magnetism.  RENT  BY  A  MAGNET. 


POLARITY  OF  A   HELIX 


389 


FIGURE  408.  —  LINES 
OF  FORCE  THROUGH  A 
LOOP. 


This  experiment  shows  that  a  circular  current  acts  like 
a  disk  magnet,  whose  poles  are  its  faces.  The  lines 
of  force  surrounding  the  conductor  in  this  form  pass 
through  the  circle  and  around  from  one  face  to  the  other 
through  the  air  outside  the  loop.  The 
north-seeking  side  is  the  one  from 
which  the  lines  issue ;  and  to  an  ob- 
server looking  toward  the  side,  the 
current  flows  around  the  loop  counter- 
clockwise (Fig.  408). 

If  instead  of  a  single  turn  we  take  a 
long  insulated  wire  and  coil  it  into  a 
number  of  parallel  circles  close  to- 
gether, the  magnetic  effect  will  be  in- 
creased. Such  a  coil  is  called  a  helix 
or  solenoid ;  and  the  passage  of  an  electric  current  through 
it  gives  to  it  all  the  properties  of  a  cylindrical  bar  magnet. 

Thread  a  loose  coil  of  copper  wire  through  holes  in  a  sheet  of  mica, 
so  that  each  turn  lies  half  on  one  side  and  half  on  the  other  (Fig.  409). 

Place  horizontally  and  scatter  fine 
iron  filings  evenly  over  the  mica. 
Send  a  strong  current  through  the 
coil  and  gently  tap  the  mica.  The 
filings  will  gather  in  the  general 
direction  of  the  lines  of  force 
•  c  through  the  helix. 

481.  Polarity  of  a  Helix.— 

The  polarity  of  a  helix  may 
be  determined  by  the  follow- 
ing rule: 

Crrasp  the  coil  with  the  right  hand  so  that  the  fingers  point 
in  the  direction  of  the  current  ;  the  north  pole  will  then  be  in 
the  direction  of  the  extended  thumb. 


FIGURE  409.  —  FIELD  IN  HELIX. 


390 


ELECTRIC  CURRENTS 


FIGURE  410.  —  ACTION  BETWEEN 
Two  CIRCUITS. 


482.   Mutual  Action  of  Two  Currents.  —  Make  a  rectangular 
coil  of  insulated  copper  wire  by  winding  four  or  five  layers  around 

the  edge  of  a  board  about  25  cm.  square. 
Slip  the  wire  off  the  board  and  tie  the 
parts  together  in  a  number  of  places 
with  thread.  Bend  the  ends  at  right 
angles  to  the  frame,  remove  the  insula- 
tion, and  give  them  the  shape  shown  in 
F  igure  41 0 .  Suspend  the  wire  f  ram  e  by 
a  long  thread  so  that  the  ends  dip  into 
the  mercury  cups. 

Make  a  second  similar  but  smaller 
coil  and  connect  it  in  the  same  circuit 
with  the  rectangular  coil  and  a  battery. 
First.  Hold  the  coil  HK  with  its 
plane  perpendicular  to  the  plane  of  the 
coil  EF,  with  its  edge  H  parallel  to  F, 
and  with  the  currents  in  these  two  ad- 
jacent portions  flowing  in  the  same  direction.  The  suspended  coil  will 
turn  upon  its  axis,  the  edge  F  approaching  H,  as  if  it  were  attracted. 

Second.  Reverse  HK  so  that  the  currents  in 
the  adjacent  portions  K  and  F  flow  in  opposite 
directions.  The  edge  Fof  the  suspended  coil  will 
be  repelled  by  K. 

Third.  Hold  the  coil  HK  within  EF,  so  that 
their  lower  sides  form  an  angle.  EF^vill  turn 
until  the  currents  in  its  lower  side  are  parallel 
with  those  in  H,  and  flowing  in  the  same  direction. 
Mount  a  long  flexible  helix  as  in  Figure  411, 
with  the  free  end  just  dipping  into  the  mercury 
in  the  glass  cup.  Pass  a  sufficient  current  through 
it ;  it  will  shorten  because  of  the  attraction  be- 
tween parallel  turns,  until  the  lower  end  leaves 

the  mercury  and  breaks  the  circuit.     It  will  then         FIGURE    41 1.  

lengthen  and  close  the  circuit  ready  for  another    ATTRACTION  BETWEEN 
oscillation.  TURNS. 

These  facts  may  be  summarized  in  the  following  laws  of 
action  between  currents: 


MAGNETIC  FIELDS  ABOUT  PARALLEL   CURRENTS    391 


Mv*«|ii! 


#/4fta/? v  "v*~  :-•-•>:  ->T33M  :M>vvA < 

liM^^i^SISli 


I.  Parallel     cur- 
rents flowing  in  the 
same    direction   at- 
tract. 

II.  Parallel    cur- 
rents flowing  in  op- 
posite directions  re- 
pel. 

III.  Currents   t 

FIGURE  412. —  MAGNETIC  FIELD  ABOUT  PARAL- 

matong     an     angle         LEL  CURRENTS  IN  THE  SAME  DIRECTION. 
with  each  other  tend 

to    become    parallel   and   to    flow   in   the   same   direc- 
tion. 

483.  Magnetic  Fields  about  Parallel  Currents.  —  Figure  412 
was  made  from  a  photograph  of  the  magnetic  field  about 
two  parallel  currents  in  the  same  direction  perpendicular 
to  the  figure.  Many  of  these  lines  of  force  surround  both 
wires,  and  it  is  the  tension  along  them  that  draws  the 
wires  together.  Figure  413  was  made  from  a  photograph 

of  the  field  when 
the  currents  were 
in  opposite  direc- 
tions. The  lines  of 
force  are  crowded 
together  between 
the  wires,  and  their 
reaction  in  their 
effort  to  recover 


....  JSplfi 

:~vkv>^     their  normal  posi- 

~H&r*">;>fS>Vif3l      A.  „ 

tion      forces      the 


FIGURE  413.  —  MAGNETIC  FIELD  ABOUT  PARALLEL 
CURRENTS  IN  OPPOSITE  DIRECTIONS. 


wires  apart. 


392  ELECTRIC  CURRENTS 

VI.  ELECTROMAGNETS 

484.   Effect  of  Introducing  Iron  into  a  Solenoid.  —  Fill  the 

lower  half  of  the  helix  of  §  480  with  soft  straight  iron  wires,  and 
again  pass  the  same  current  as  before  through  the  coil.  The  mag- 
netic field  will  be  greatly  strengthened  by  the  iron. 

A  helix  of  wire  about  an  iron  core  is  an  electromagnet. 
It  was  first  made  by  Sturgeon  in  1825.  The  presence  of 
the  iron  core  greatly  increases  the  number  of  lines  of  force 
threading  through  the  helix  from  end  to  end,  by  reason  of 


FIGURE  414.  —  IRON  INCREASES  MAGNETIC  LINES. 

the  greater  permeability  of  iron  as  compared  with  air 
(Fig.  414).  If  the  iron  is  omitted,  there  are  not  only 
fewer  lines  of  force,  but  because  of  their  leakage  at  the 
^ides  of  the  helix,  fewer  traverse  the  entire  length  of 
the  coil. 

The  soft  iron  core  of  an  electromagnet  does  not  show 
much  magnetism  except  while  the  current  is  flowing 
through  the  magnetizing  coil.  The  loss  of  magnetism  is 
not  quite  complete  when  the  current  is  interrupted;  the 
small  amount  remaining  is  called  residual  magnetism. 

485.   Relation  between  a  Magnet  and  a  Flexible  Conductor. 

—  Iron  filings  arranged  in  circles  about  a  conductor  may  be  regarded 
as  flexible  magnetized  iron  winding-  itself  into  a  helix  around  the 
current;  conversely,  a  flexible  conductor,  carrying  a  current,  winds 


James  Clerk-Maxwell  (1831-1879)  was  a  remarkable  physi- 
cist and  mathematician.  He  was  born  in  Edinburgh  and  studied 
in  the  University  of  that  city.  Later  he  attended  the  University 
of  Cambridge,  graduating  from  there  in  1854.  In  1856  he  be- 
came professor  of  natural  philosophy  at  Marischal  College,  Aber- 
deen, and  in  1860  professor  of  physics  and  astronomy  at  King's 
College,  London.  In  1871  he  was  appointed  professor  of  experi- 
mental physics  in  Cambridge.  His  contributions  to  the  kinetic 
theory  of  gases,  the  theory  of  heat,  dynamics,  and  the  mathemati- 
cal theory  of  electricity  and  magnetism  are  imperishable  monu- 
ments to  his  great  genius  and  wonderful  insight  into  the  mysteries 
of  nature. 


THE  HORSESHOE  MAGNET 


393 


itself  around  a  straight  bar  magnet.  The  flexible  conductor  of 
Figure  415  may  be  made  of  tinsel  cord  or  braid.  Directly  the  circuit  is 
closed,  the  conductor  winds 
slowly  around  the  vertical  mag- 
net;  if  the  current  is  then  re- 
versed, the  conductor  unwinds 
and  winds  up  again  in  the  re- 
verse direction. 

486.  The  Horseshoe  Mag- 
net. —  The  form  given  to 
an  electromagnet  depends 
on  the  use  to  which  it  is  to 
be  put.  The  horseshoe  or 
U-shape  (Fig.  416)  is  the 
most  common.  The  ad- 
vantage of  this  form  lies 
in  the  fact  that  all  lines  of 
magnetic  force  are  closed 
curves,  passing  through  the 
core  from  the  south  to  the 
north  pole,  and  completing  the  circuit  through  the  air  from 
the  north  pole  back  to  the  south  pole.  The  U-shape  lessens 
the  distance  through  the  air  and  thus  increases  the  number 

of  lines.  Moreover,  when  an  iron 
bar,  called  the  armature,  is  placed 
across  the  poles,  the  air  gap  is  re- 
duced to  a  thin  film,  the  number 
of  lines  is  increased  to  a  maximum 
with  a  given  current  through  the 
helix,  and  the  magnet  exercises 
the  greatest  pull  on  the  arma- 
ture. 

When  the  armature  is  in  contact  with  the  poles,  the 
magnetic   circuit   is   all  iron,  and    is  said  to  be  a  closed 


FIGURE    415.  —  FLEXIBLE    CONDUCTOR 
WINDS  ITSELF  AROUND  A  MAGNET. 


II 

FIGURE  416.  —  HORSESHOE 
MAGNET. 


394 


ELECTRIC   CURRENTS 


magnetic  circuit.  The  residual  magnetism  is  then  much 
greater  than  in  the  case  of  an  open  magnetic  circuit  with 
an  air  gap. 

Bring  the  armature  in  contact  with  the  iron  poles  of  the  core,  and 
close  the  electric  circuit ;  after  the  circuit  is  opened,  the  armature  will 
still  cling  to  the  poles  and  can  be  removed  only  with  some  effort. 
Then  place  a  piece  of  thin  paper  between  the  poles  and  the  armature. 
After  the  magnet  has  again  been  excited  and  the  circuit  opened,  the 
armature  will  not  now  "  stick."  The  paper 
makes  a  thin  air  gap  between  the  poles  of  the 
magnet  and  the  armature,  and  thus  reduces 
the  residual  magnetism. 

487.  Applications  of  Electromagnets. — 

The  uses  to  which  electromagnets  are  put  in 
the  applications  of  electricity  are  so  numerous 
that  a  mere  reference  to  them  must  suffice. 
The  electromagnet  enters  into  the  construc- 
tion of  electric  bells,  telegraph  and  telephone 
instruments,  dynamos,  motors,  signaling  de- 
vices, etc.  It  is  also  extensively  used  in  lift- 
ing large  masses  of  iron,  such  as  castings, 
rolled  plates,  pig  iron,  and  steel  girders  (Fig. 
417).  The  lifting  power  depends  chiefly  on 
the  cross  section  of  the  iron  core  and  on  the 
ampere  turns  •  that  is,  on  the  product  of  the 

number  of   amperes  of  current   and  the  number  of  turns  of   wire 

wound  on  the  magnet. 

VII.   MEASURING  INSTRUMENTS 

488.  The  Galvanometer.  —  The  instrument  for  the  com- 
parison of  currents  by  means  of  their  magnetic  effects  is 
called  a  galvanometer.  A  galvanoscope  (§  446)  becomes 
a  galvanometer  by  providing  it  with  a  scale  so  that  the 
deflections  may  be  measured.  If  the  galvanometer  is 
calibrated,  so  as  to  read  directly  in  amperes,  it  is  called  an 
ammeter.  In  very  sensitive  instruments  a  small  mirror  is 


FIGURE  417.  —  LIFTING 
MAGNET. 


THE  D'ARSONVAL  GALVANOMETER 


395 


FIGURE  418.  —  PLAN  OF  D'AR- 
SONVAL  GALVANOMETER. 


attached  to  the  movable  part  of  the  instrument;  it  is  then 
called  a  mirror  galvanometer.  Sometimes  a  beam  of  light 
from  a  lamp  is  reflected  from  this 
small  mirror  back  to  a  scale,  and 
sometimes  the  light  from  a  scale 
is  reflected  back  to  a  small  tele- 
scope, by  means  of  which  the  de- 
flections are  read.  In  either  case 
the  beam  of  light  then  becomes  a 
long  pointer  without  weight. 

489.  The  d'Arsonval  Galvanom- 
eter—  One  of  the  most  useful 
forms  of  galvanometer  is  the 
d'Arsonval.  The  plan  of  it'  is 
shown  in  Figure  418  and  a  com- 
plete working  instrument  in  Figure  419. 
Between  the  poles  of  a  strong  permanent 
magnet  of  the  horseshoe  form  swings  a 
rectangular  coil  of  fine  wire  in  such  a  way 
that  the  current  is  led  into  the  coil  by  the 
fine  suspending  wire,  and  out  by  the  wire 
spiral  running  to  the  base.  A  small  mirror 
is  attached  to  the  coil  to  reflect  light  from 
a  lamp  or  an  illuminated  scale.  •  Some- 
times the  coil  carries  a  light  aluminum 
pointer,  which  traverses  a  scale.  Inside 
the  coil  is  a  soft  iron  tube  supported  from 
the  back  of  the  case.  It  is  designed  to 
concentrate  the  lines  of  force  in  the  narrow 
openings  between  it  and  the  poles  of  the 
magnet. 

In  the  d'Arsonval  galvanometer  the  coil  is  movable  and 
the  magnet  is  fixed.     Its  chief  advantages  are  simplicity 


FIGURE  419.— 
SIMPLE  D'ARSON- 
VAL GALVANOM- 
ETER. 


396  ELECTRIC  CURRENTS 

of  construction,  comparative  independence  of  the  earth's 
magnetic  field,  and  the  quickness  with  which  the  coil 
comes  to  rest  after  deflection  by  a  current  through  it. 

490.  The  Voltmeter. 
—  The  voltmeter  is  an 
instrument  designed  to 
measure  the  difference 
of  potential  in  volts. 
For  direct  currents  the 
most  convenient  port- 
able voltmeter  is  made 
on  the  principle  of  the 
d'Arsonval  galvanom- 
eter. One  of  the  best- 
FIGURE  420. — VOLTMETER. 

known  instruments  of 

this  class  is  shown  in  Figure  420.  The  interior  is  rep- 
resented by  Figure  421,  where  a  portion  of  the  in- 
strument is  cut  away  to  show  the  coil  and  the  springs. 
The  current  is  led  in  by  one  spiral  spring  and  out  by 
the  other.  Attached  to  the 
coil  is  a  very  light  aluminum 
pointer,  which  moves  over 
the  scale  seen  in  Figure  420 
where  it  stands  at  zero.  Soft 
iron  pole  pieces  are  screwed 
fast  to  the  poles  of  the  per- 
manent magnet,  and  they  are 
so  shaped  that  the  divisions 
of  the  scale  in  volts  are  equal. 

In  circuit  with  the  coil  of 
_  .  .«..•'.     FIGURE  421.  —  INSIDE  OF  VOLTMETER. 

the  instrument  is  a  coil  of 

wire  of  high  resistance,  so  that  when  the  voltmeter  is  placed 
in  circuit,  only  a  small  current  will  flow  through  it. 


DIVIDED   CIRCUITS  —  SHUNTS  397 

491.  The  Ammeter,  designed  to  measure  electric  currents 
in  amperes,  is  very  similar  in  construction  to  the  voltmeter. 
A  low  resistance  shunt  is  connected  across  the  terminals 
of  the  coil  to  carry  the  main  current,  so  that  when  the 
ammeter  is  placed  in  circuit,  it  will  not  change  the  value 
of  the  current  to  be  measured. 

Questions 

1.  Why  must  the  article  to  be  electroplated  be  attached  to  the 
negative  pole  of  the  generator  ? 

2.  How  can  you  determine  the  positive  pole  of  a  storage  battery? 

3.  Why  will  it  ruin  a  pocket  ammeter  to  connect  its  terminals  to 
the  poles  of  a  storage  battery  ? 

4.  Why  does  the  heating  in  an  electric  circuit  manifest  itself  at  a 
point  where  the  conductor  is  defective? 

5.  If  in  Figure  415  the  north  pole  of  the  magnet  is  at  the  top, 
which  way  will  the  flexible  tinsel  wrap  around  the  magnet? 

6.  Why  should  the  ammeter  be  of  low  resistance  and  the  volt- 
meter of  high  resistance  ? 

7.  Why  should  a  Daniell  cell  when  not  in  use  either  be  taken 
down  or  placed  on  closed  circuit  ? 

8.  Why  must   the  wire   used  in  winding  an   electromagnet   be 
insulated  ? 

9.  What  is  the  least  number  of  gravity  cells  that  might  be  used 
to  charge  a  storage  battery  and  how  must  they  be  connected? 

10.  What  would  be  the  harm  of  leaving  a  dry  cell  on  a  closed 
circuit  ? 

11.  Why  will  a  low  resistance  voltmeter  give  the  E.M.F.  of  a 
storage  battery  more  nearly  correct  than  it  will  that  of  a  dry  cell  ? 

12.  Why  will  cotton-wound  wire  be  sufficiently  insulated  for  a 
battery,  but  not  for  a  Holtz  machine  ? 

49£  Divided  Circuits  —  Shunts.  —  When  the  wire  leading 
from  any  electric  generator  is  divided  into  two  branches, 
as  at  B  (Fig.  422),  the  current  also  divides,  part  flowing 


398 


ELECTRIC  CURRENTS 


FIGURE  422.  —  DIVIDED  CIRCUIT. 


by  one  path  and  part  by  the  other.     The  sum  of  these  two 
currents  is  always  equal  to  the  current  in  the  undivided 

part  of  the  circuit,  since  there 
is  no  accumulation  of  electric- 
ity at  any  point.  Either  of 
the  branches  between  B  and 
A  is  called  a  shunt  to  the 
other,  and  the  currents  through  them  are  inversely  propor- 
tional to  their  resistances. 

493.  Resistance  of  a  Divided  Circuit.  —  Let  the  total  resist- 
ance between  the  points  A  and  B  (Fig.  422)  be  represented  by  R, 
that  of  the  branch  BmA  by  r,  and  of  BnA  by  rr.  The  conductance  of 
BA  equals  the  sum  of  the  conductances  of  the  two  branches ;  and,  as 
conductance  is  the  reciprocal  of  resistance,  the  conductances  of  BA, 

BmA,   and  BnA    are  — ,   -,  and   —   respectively; 
Mr  r 

rr' 


then    -    =     +     . 
R      r      r' 


From  this  we  derive  R  = 


To  illustrate,  let  a  galvanometer 


r  +  r' 

whose  resistance  is  100  ohms  have  its  binding  posts  connected  by  a 
shunt  of  50  ohms  resistance;  then  th$  total  resistance  of  this  divided 


circuit  is 


100  x  50 


=  331  ohms. 


B\ 
rowr^ 


100  +  50 

The  introduction  of  a  shunt 
always  lessens  the  resistance  be- 
tween the  points  connected. 

494.  Loss  of  Potential 
along  a  Conductor.  —  Stretch 
a  fine  wire  of  fairly  high  resist- 
ance, such  as  a  German  silver 
No.  30,  along  the  edge  of  a  meter 
stick  (Fig.  423).  Connect  the 
ends  P  and  Q  to  a  storage  cell 
with  a  contact  key  in  circuit. 
At  P  connect  a  galvanometer  in  circuit  with  a  high  resistance  R  and 
a  slide  contact  S.  The  galvanometer  will  indicate  the  difference  of 
potential  between  P  and  S,  the  point  of  contact  on  PQ.  If  S  be 
placed  successively  on  PQ  at  10  cm.,  20  cm.,  30  cm.,  etc.,  from  P,  and 


FIGURE  423.  —  FALL  OF  POTENTIAL  ALONG 
A  CONDUCTOR. 


WHEATSTONE'S  BRIDGE 


399 


the  galvanometer  reading  be  recorded  each  time,  the  ratio  of  the 
readings  will  be  as  1:2:3,  etc.  Since  resistance  is  proportional  to 
length,  these  potential  differences  are  as  the  resistances  of  the  succes- 
sive lengths  of  the  wire  PQ,  or  the  loss  of  potential  is  proportional  to  the 
resistance  passed  over. 

This  is  equivalent  to  another  statement  of  Ohm's  law ; 

IT 

for  since  1=  — ,  and  the  current  through  the  conductor  is 
H> 

the  same  at  all  points,  it  follows  that  E  must  vary  as  R  to 
make  I  constant. 


495.  Wheatstone's  Bridge.  —  The  Wheatstone's  Bridge  is  a  de- 
vice for  measuring  resistances.  The  four  conductors,  Rv  Rz,  Rz,  R4 
are  the  arms  and  BD  the  bridge  (Fig. 
424).  When  the  circuit  is  closed  by 
closing  the  key  Kv  the  current  divides 
at  A,  the  two  parts  reuniting  at  C. 
The  loss  of  potential  along  ABC  is  the 
same  as  along  ADC.  If  no  current 
flows  through  the  galvanometer  G 
when  the  key  K}  is. also  closed,  then 
there  is  no  potential  difference  between 
B  and  D  to  produce  a  current.  Under 
these  conditions  the  loss  of  potential 
from  A  to  B  is  the  same  as  from  A 
to  D.  We  may  then  get  an  expression 
for  these  potential  differences  and 
place  them  equal  to  each  other. 

Let  7j  be  the  current  through  Rl;  it  will  also  be  the  current 
through  R±,  because  none  flows  across  through  the  galvanometer. 
Also  let  72  be  the  current  through  the  branch  A  DC.  Then  the  poten- 
tial difference  between  A  and  B  by  Ohm's  law  (§  471)  is  equal  to  RJi ; 
and  the  equal  potential  difference  between  A  and  D  is  Rzly  Equating 

these  expressions, 

R1ll  -  R2J2 (a) 

In  the  same  way  the  equal  potential  differences  between  B  and  C 
and  D  and  C  give 


FIGURE  424.  —  WHEATSTONE'S 
BRIDGE. 


400  ELECTEJC  CURRENTS 

Dividing  (a)  by  (6)  gives 


-2     ......    (Equation  38) 


In  practice  three  of  the  four  resistances  are  adjustable  and  of 
known  value.  They  are  adjusted  until  the  galvanometer  shows  no 
deflection  when  the  key  K\  is  closed  after  key  Ky  The  value  of  the 
fourth  resistance  is  then  derived  from  the  relation  in  Equation  38. 

Problems 

1.  Calculate  the  resistance  of  200  ft.  of  copper  wire  (k  =  10.19) 
No.  24  (diameter  =  0.0201  in.). 

2.  A  coil  of  iron  wire  (k  =  61.3)  is  to  have  a  resistance  of  25  ohms. 
The  diameter  of  the  wire  used  is  0.032  in.     How  many  feet  will  it  re- 
quire ? 

3.  What  diameter  must  a  copper  trolley  (k  =  10.19)  have  so  that 
the  resistance  will  be  half  an  ohm  to  the  mile  ? 

4.  A  current  of  one  ampere  deposits  by  electrolysis  1.1833  g.  of 
copper  in  an  hour.     How  long  will  it  take  a  current  of  5  amperes  to 
deposit  a  kilogram  of  copper  ? 

5.  A  current  of  two  amperes  passes  through  a  solution  of  silver 
nitrate  for  one  hour.     How  much  silver  will  be  deposited  ? 

6.  A  current  of  10  amperes  is  sent  through  a  resistance  of  4  ohms 
for  10  minutes.     How  many  calories  of  heat  are  generated  ? 

7.  What  current  will  6  dry  cells  connected  in  series,  each  having 
an  E.  M.  F.  of  1.5  volts  and  an  internal  resistance  of  0.1  ohm,  give 
through  an  external  resistance  of  2  ohms  ? 

8.  A  certain  dry  cell  has  a  voltage  of  1.5  volts  and  when  tested 
with  an  ammeter  gives  20  amperes.     What  is  its  internal  resistance  ? 

9.  A  certain  lamp  requires  0.5  ampere  current  and  an  E.  M.  F.  of 
110  volts  to  light  it.     What  is  its  resistance  ? 

10.  A  projection  lantern  requires  a  current  of  15  amperes.  The 
voltage  of  the  supply  is  110  volts  and  the  loss  in  the  lamp  is  40  volts. 
What  resistance  must  be  inserted  in  the  line  to  the  lantern? 


Joseph  Henry  (1797-1878)  was  born  at  Albany,  New  York. 
The  reading  of  Gregory's  Lectures  on  Experimental  Philosophy 
interested  him  so  greatly  in  science  that  he  began  experimenting. 
In  1829  he  constructed  his  first  electromagnet.  In  1832  he  was 
appointed  professor  of  natural  philosophy  at  Princeton  College. 
In  1846  he  became  secretary  of  the  Smithsonian  Institution  in 
Washington.  It  is  almost  certain  that  he  anticipated  Faraday's 
great  discovery  of  magneto-electric  induction  by  a  whole  year 
but  failed  to  announce  it.  His  principal  investigations  were  in 
electricity  and  magnetism,  and  chiefly  in  the  realm  of  induced 
currents. 


Michael  Faraday,  1791-1867,  was  born  near  London,  England. 
He  was  the  son  of  a  blacksmith  and  received  but  little  schooling, 
being  apprenticed  to  a  bookbinder  when  only  thirteen  years  of 
age.  While  employed  in  the  bindery  he  became  interested  in 
reading  such  scientific  books  as  he  found  there.  Later  he  applied 
to  Sir  Humphry  Davy  for  consideration  and  was  made  Davy's 
assistant.  From  this  time  his  rise  was  rapid ;  in  1816  he  published 
his  first  scientific  memoir;  in  1824  he  became  a  member  of  the 
Royal  Society;  in  1825  he  was  elected  director  of  the  Royal 
Institution ;  in  1831  he  announced  the  discovery  of  magneto- 
electric  induction,  the  most  important  scientific  discovery  of  any 
age.  In  1833  he  was  elected  professor  of  chemistry  in  the  Royal 
Institution.  He  was  a  remarkable  experimenter  and  a  most  inter- 
esting lecturer,  and  amid  all  his  wonderful  achievements,  he  was 
utterly  wanting  in  vanity. 


CHAPTER  XIII 


FIGURE   425.  —  FARADAY'S  ORIGINAL 
EXPERIMENT  ON  INDUCED  E.  M.  F. 


ELECTROMAGNETIC  INDUCTION 
I.    FAEADAY'S  DISCOVERIES 

496.  Electromotive  Force  Induced  by  a  Magnet.  —  Wind  a 
large  number  of  turns  of  fine  insulated  wire  around  the  armature  of  a 
horseshoe  magnet,  leaving  the  ends  of  the  iron  free  to  come  in  contact 
with  the  poles  of  the  permanent 
magnet.  Connect  the  ends  of  the 
coil  to  a  sensitive  galvanometer, 
the  armature  being  in  contact 
with  the  magnetic  poles,  as  shown 
in  Figure  425.  Keeping  the  mag- 
net fixed,  suddenly  pull  off  the  ar- 
mature. The  galvanometer  will 

show  a  momentary  current.  Suddenly  bring  the  armature  up  against 
the  poles  of  the  magnet;  another  momentary  current  in  the  reverse 
direction  will  flow  through  the  circuit.  This  experiment  illustrates 

Faraday's  original  method 
of  producing  an  electric 
current  through  the 
agency  of  magnetism. 

Connect  a  coil  of  insu- 
lated copper  wire,  at  least 
fifty  turns  of  No.  24,  in 
circuit  with  a  d'Arsonval 
galvanometer  (Fig.  426). 
Thrust  quickly  into  the 
coil  the  north  pole  of  a 
bar  magnet.  The  galva- 
nometer will  show  a  transient  current,  which  will  flow  only  during 
the  motion  of  the  magnet.  When  the  magnet  is  suddenly  withdrawn 

401 


FIGURE  426.  —  CURRENT  INDUCED  BY  THRUST- 
ING MAGNET  INTO  COIL. 


402  ELECTROMAGNETIC  INDUCTION 

a  transient  current  is  produced  in  the  opposite  direction  to  the  first 
one.  If  the  south  pole  be  thrust  into  the  coil,  and  then  withdrawn, 
the  currents  in  both  cases  are  the  reverse  of  those  with  the  north  pole. 
If  we  substitute  a  helix  of  a  smaller  number  of  turns,  or  a  weaker  bar 
magnet,  the  deflection  will  be  less. 

The  morrientary  electromotive  forces  generated  in  the 
coil  are  known  as  induced  electromotive  forces,  and  the  cur- 
rents as  induced  currents.  They  were  discovered  by 
Faraday  in  1831. 

497.  Laws  of  Electromagnetic  Induction.  —  When  the 
armature  in  the  first  experiment  of  the  last  article  is  in 
contact  with  the  poles  of  the  magnet,  the  number  of  lines 
of  force  passing  through  the  coil,  or  linked  with  it,  is  a 
maximum.  When  the  armature  is  pulled  away,  the  num- 
ber of  magnetic  lines  threading  through  the  coil  rapidly 
diminishes. 

When  the  magnet  in  the  second  experiment  is  thrust 
into  the  coil,  it  carries  its  lines  of  force  with  it,  so  that 
some  of  them  at  least  encircle,  or  are  linked  with,  the 
wires  of  the  coil.  In  both  experiments  an  electromotive 
force  is  generated  only  while  the  number  of  lines  so  linked 
with  the  coil  is  changing.  The  E.M.F.  is  generated  in 
the  coil  in  accordance  with  the  following  laws  : 

I.  An  increase  in  the  number  of  lines  of  force  linked 
with  a  conducting  circuit  produces  an  indirect  E.  M.  F. ; 
a  decrease  in  the  number  of  lines  produces  a  direct  E.  M.  F. 

IT.  The  induced  E.M.F.  at  any  instant  is  equal  to  the 
rate  of  increase  or  decrease  in  the  number  of  lines  of  force 
linked  with  the  circuit. 

A  direct  E.M.F.  has  a  clockwise  direction  to  an  observer 
looking  along  the  lines  of  force  of  the  magnet ;  an  indirect 
E.  M.  F.  is  one  in  the  opposite  direction.  Thus,  in  Figure 


INDUCTION  BY  CURRENTS 


403 


FIGURE  427.  —  DIRECTION  OF  IN- 
DUCED E.M.F. 


427  the  north  pole  of  the  magnet  is  moving  into  the  coil 

in  the  direction  of  the  arrow ;    there   is  an  increase  in 

the  number  of  lines  passing 

through  the  coil,  and  the  E. 

M.F.  and  current  are  indirect 

or  opposite  watch  hands,  as 

shown  by  the  arrows  on  the 

coil,  to  an   observer  looking 

at  the  coil   in  the  direction 

of  the  arrow  on  the  magnet. 

498.    Induction  by  Currents. 

—  Connect  the  S  coil  of  Figure  428 

to  a  d'Arsonval   galvanometer,  and  a  second  smaller  coil  P  to  the 

terminals  of  a  battery.     If  the  current  through  P  is  kept  constant, 

when  P  is  made  to  approach 
S  an  E.  M.  F.  is  generated  in 
S  tending  to  send  a  current 
in  a  direction  opposite  to  the 
current  around  P;  removing 
•the  coil  P  generates  an  oppo- 
site E.  M.  F.  These  E.  M.  F.'s 
act  in  S  only  so  long  as  P  is 
To  moving. 

battery  Next  insert  the  coil  P  in  S 

with  the  battery  circuit  open. 
If  then  the  battery  circuit  is 
closed,  the  needle  of  the  gal- 
vanometer will  be  deflected, 
fi|!;::  but  will  shortly  come  again  to 
rest  at  zero.  The  direction 
of  this  momentary  current  is 
opposite  to  that  in  P.  Open- 
ing the  battery  circuit  produces 
another  momentary  current 
through  S  but  in  the  opposite 

direction.     Increasing  and  decreasing  the  current  through  P  has  the 

same  effect  as  closing  and  opening  the  circuit. 


FIGURE  428.  —  CURRENTS  INDUCED  BY 
ANOTHER  CURRENT. 


404  ELECTROMAGNETIC  INDUCTION 

If  while  P  is  inside  S  with  the  battery  circuit  closed,  a  bar  of  soft 
iron  is  placed  within  P,  there  is  an  increase  of  magnetic  lines  through 
both  coils  and  the  inductive  effect  in  S  is  the  same  as  that  produced 
by  closing  the  circuit  through  P. 

The  coil  P  is  called  the  primary  and  S  the  secondary 
coil.  The  results  may  be  summarized  as  follows: 

I.  A  momentary  current  in  the  opposite  direction  is 
induced  in  the  secondary  conductor  by  the  approach,  the 
starting,  or  the  strengthening  of  a  current  in  the  primary. 

II.  A  momentary  current  in  the  same  direction  is  in- 
duced in  the  secondary  by  the  receding,  the  stopping,  or 
the  weakening  of  the  current  in  the  primary. 

The  primary  coil  becomes  a  magnet  when  carrying  an 
electric  current  (§  480)  and  acts  toward  the  secondary  coil 
as  if  it  were  a  magnet.  The  soft  iron  increases  the 
magnetic  flux  through  the  coil  and  so  increases  the  in- 
duction. 

499.  Lenz's  Law.  —  When  the  north  pole  of  the  magnet  is 
thrust  into  the  coil  of  Figure  427,  the  induced  current  flow- 
ing in  the  direction  of  the  arrows  produces  lines  of  force 
running  in  the  opposite  direction  to  those  from  the  magnet 
(§  479).  These  lines  of  force  tend  to  oppose  the  change 
in  the  magnetic  field  within  the  coil,  or  the  magnetic  field 
set  up  by  the  coil  opposes  the  motion  of  the  magnet. 

Again,  when  the  primary  coil  of  Figure  428  is  inserted 
into  the  secondary,  the  induced  current  in  the  latter  is 
opposite  in  direction  to  the  primary  current,  and  parallel 
currents  in  opposite  directions  repel  each  other.  In  every 
case  of  electromagnetic  induction  the  change  in  the  mag- 
netic field  which  produces  the  induced  current  is  always 
opposed  by  the  magnetic  field  due  to  the  induced  current 
itself. 


JOSEPH  HENRY'S  DISCOVERY 


406 


The  law  of  Lenz  respecting  the  direction  of  the  induced 
current  is  broadly  as  follows: 

The  direction  of  an  induced  current  is  always  such 
that  it  produces  a  magnetic  field  opposing  the  motion  or 
change  which  induces  the  current. 


II.    SELF-INDUCTION 

500.  Joseph  Henry's  Discovery.  —  Joseph  Henry  discov- 
ered that  a  current  through  a  helix  with  parallel  turns 
acts  inductively  on  its  own  circuit,  producing  what  is 
often  called  the  extra  current,  and 
a  bright  spark  across  the  gap  when 
the  circuit  is  opened.  The  effects 
are  not  very  marked  unless  the 
helix  contains  a  soft  iron  core. 

Let  a  coil  of  wire  be  wound 
around  a  wooden  cylinder'  (Fig. 
429).  When  a  current  is  flowing 
through  this  coil,  some  of  the  lines 
of  force  around  one  turn,  as  A, 
thread  through  adjacent  turns  ;  if  the  cylinder  is  iron,  the 
number  of  lines  threading  through  adjacent  turns  will  be 
largely  increased  on  account  of  the  superior  permeability 
of  the  iron  (§  401).  Hence,  at  the  make  of  the  circuit, 
the  production  of  magnetic  lines  threading  through  the 
parallel  turns  of  wire  induces  a  counter-E.M.F.  opposing 
the  current.  The  result  is  that  the  current  does  not  reach 
at  once  the  value  given  by  Ohm's  law.  At  the  break  of 
the  circuit,  the  induction  on  the  other  hand  produces  a 
direct  E.M.F.  tending  to  prolong  the  current.  With 
many  turns  of  wire,  this  direct  E.M.F.  is  high  enough 
•to  break  over  a  short  gap  and  produce  a  spark. 


FIGURE  429.  —  SELF-INDUC- 
TION. 


406 


ELECTS OMA  GNETIC  IND  UCTION 


501.  Illustrations  of  Self-induction.  —  Connect  two  or  three 
cells  in  series.  Join  electrically  a  flat  file  to  one  pole  and  a  piece  of 
iron  wire  to  the  other.  Draw  the  end  of  the  wire  lengthwise  along 
the  file ;  some  sparks  will  be  visible,  but  they  emit  little  light.  Now 
put  an  electromagnet  in  the  circuit  to  increase  the  self-induction ; 
the  sparks  are  now  much  longer  and 
brighter. 

Connect  as  shown  in  Figure  430  a  large 
electromagnet  M,  a  storage  battery  B,  a 
circuit  breaker  K,  and  an  incandescent 
lamp  L  of  such  a  size  that  the  battery 
alone  will  light  it  to  nearly  its  full  candle 
power.  The  circuit  divides  between  the 
lanip  and  the  electromagnet,  and  since  the 
latter  is  of  low  resistance,  when  the  cur- 
rent reaches  its  steady  state  most  of  it  will 
go  through  the  coils  of  the  magnet,  leaving 
the  lamp  at  only  a  dull  red.  At  the  in- 
stant when  the  circuit  is  closed,  the  self- 
induction  of  the  magnet  acts  against  the 
current  and  sends  most  of  it  around 
through  the  lamp.  It  accordingly  lights 
up  at  first,  but  quickly  grows  dim  as  the  current  rises  to  its  steady 
value  in  M. 

Now  open  the  circuit  breaker  K,  cutting  off  the  battery.  The  only 
closed  circuit  is  now  the  one  through  the  magnet  and  the  lamp ;  but 
the  energy  stored  in  the  magnetic  field  of  the  electromagnet  is  then 
converted  into  electric  energy  by  means  of  self-induction,  and  the 
lamp  again  lights  up  brightly  for  a  moment. 


M 

) 

4 

1 

1 

B 

1 

1 

1 

K 

1— 

FIGURE  430.  —  LAMP 
LIGHTED  BY  SELF-INDUCTION 
OF  MAGNET. 


III.     THE  INDUCTION  COIL 

502.  Structure  of  an  Induction  Coil.  —  The  induction  coil 
is  commonly  used  to  give  transient  flashes  of  high  electro- 
motive force  in  rapid  succession.  A  primary  coil  of  com- 
paratively few  turns  of  stout  wire  is  wound  around  an 
iron  core,  consisting  of  a  bundle  of  iron  wires  to  avoid 
induced  or  eddy  currents  in  the  metal  of  the  core  ;  outside 


ACTION  OF  THE  COIL  407 

of  this,  and  carefully  insulated  from  it,  is  the  secondary  of 
a  very  large  number  of  turns  of  fine  wire.  The  inner  or 
primary  coil  is  connected 
to  a  battery  through  a  cir- 
cuit breaker  (Fig.  431). 
This  is  an  automatic  device 
for  opening  and  closing  the 
primary  circuit  and  is  ac- 
tuated by  the  magnetism 
of  the  iron  core.  At  the 

"make"  and  "break"  of 
.,  .  ,  FIGURE  431.  —  INDUCTION  COIL. 

the  primary  circuit  elec- 
tromotive forces  are  induced  in  the  secondary  in  accord- 
ance with  the  laws  of  electromagnetic  induction  (§  497). 
Large  induction  coils  include  also  a  condenser.  It  is 
placed  in  the  base  and  consists  of  two  sets  of  interlaid 
layers  of  tin-foil,  separated  by  sheets  of  paper  saturated 
with  paraffin.  The  two  sets  are  connected  to  two  points 
of  the  primary  circuit  on  opposite  sides  of  the  circuit 
breaker  (Fig.  432). 

503.  Action  of  the  Coil.  —  Figure  432  shows  the  arrange- 
ment of  the  various  parts  of  an  induction  coil.  The  cur- 
rent first  passes  through  the  heavy  primary  wire  PP, 
thence  through  the  spring  A,  which  carries  the  soft  iron 
block  F,  then  across  to  the  screw  5,  and  so  back  to  the 
negative  pole  of  the  battery.  This  current  magnetizes 
the  iron  core  of  the  coil,  and  the  core  attracts  the  soft  iron 
block  F,  thus  breaking  the  circuit  at  the  point  of  the 
screw  b.  The  core  is  then  demagnetized,  and  the  release 
of  F  again  closes  the  circuit.  Electromotive  forces  are 
thus  induced  in  the  secondary  coil  SS,  both  at  the  make 
and  the  break  of  the  primary.  The  high  E.M.F.  of  the 
secondary  is  due  to  the  large  number  of  turns  of  wire  in 


408 


ELECTROMAGNETIC  INDUCTION 


it  and  to  the  influence  of  the  iron  core  in  increasing  the 
number  of  lines  of  force  which  pass  through  the  entire 
coil. 

The  self-induction  of  the  primary  has  a  very  important 
bearing  on  the  action  of  the  coil.  At  the  instant  the  cir- 
cuit is  closed,  the  counter  E.M.F.  opposes  the  battery 


FIGURE  432.  —  STRUCTURE  OF  INDUCTION  COIL. 

current,  and  prolongs  the  time  of  reaching  its  greatest 
strength.  Consequently  the  E.M.F.  of  the  secondary 
coil  will  be  diminished  by  self-induction  in  the  primary. 
The  E.M.F.  of  self-induction  at  the  "break"  of  the  pri- 
mary is  direct,  and  this  added  to  the  E.M.F.  of  the  battery 
produces  a  spark  at  the  break  points  of  the  circuit  breaker. 

504.  Office  of  the  Condenser.  —  When  the  primary  circuit  of  an 
induction  coil  is  broken,  the  self-induction  tends  to  sustain  the  cur- 
rent as  if  it  had  inertia;  hence  it  jumps  the  break  as  a  spark  and 
prevents  the  abrupt  interruption  of  the  primary  current,  which  is 
essential  to  high  induction  in  the  secondary.  The  condenser  connected 
across  the  break  gap  acts  as  a  reservoir  into  which  the  current  surges 
instead  of  jumping  across  the  break.  Thus  the  spark  is  nearly  elimi- 
nated and  the  secondary  E.  M.  F.  increased. 

Further,  after  the  break,  the  condenser,  which  has  been  charged  by 
the  E.M.F.  of  self-induction,  discharges  back  through  the  primary 


EXPERIMENTS    WITH  THE  INDUCTION  COIL      409 

coil.  The  condenser  thus  causes  an  electric  recoil  in  the  current  in 
the  reverse  direction  through  the  primary,  demagnetizing  the  core 
and  increasing  the  rate  of  change  of  the  magnetic  flux,  and  so  in- 
creasing the  E.  M.  F.  in  the  secondary.  Hence,  when  the  secondary 
terminals  are  separated,  the  discharge  is  all  in  one  direction  and  occurs 
when  the  primary  current  is  broken. 

505.  Experiments  with  the  Induction  Coil.  —  1.  Physiological 

Effects.  —  Hold  in  the  hands  the  electrodes  of  a  very  small  induction 
coil,  of  the  style  used  by  physicians.  When  the  coil  is  working,  a 
peculiar  muscular  contraction  is  produced. 

The  "  shock  "  from  large  coils  is  dangerous  on  account 
of  the  high  E.M.F.  The  danger  decreases  with  the  in- 
crease in  the  rapidity  of  the  impulses  or  alternations. 
Experiments  with  induction  coils,  worked  by  alternating 
currents  of  very  high  frequency,  have  demonstrated  that 
the  discharge  of  the  secondary  up  to  .an  ampere  may  be 
taken  through  the  body  without  injury. 

2.  Mechanical  Effects.  —  Hold  a  piece  of  cardboard  between   the 
electrodes  of  an  induction  coil  giving  a  spark  3  cm.  long.     The  card 
will  be  perforated,  leaving  a  burr  on  each  side.     Thin  plates  of  any 
nonconductor  can  be  perforated  in  the  same  manner. 

3.  Chemical  Effects.  —  Place  on  a  plate  of  glass  a  strip  of  white 
blotting-paper  moistened  with  a  solution  of  potassium  iodide  (a  com- 
pound of  potassium  and  iodine)  and  starch  paste.     Attach  one  of  the 
electrodes   of  a  small  induction   coil  to  the  margin  of  the  paper. 
With  an  insulator,  handle  a  wire  leading  to  the  other  electrode,  and 
when  the  coil  is  in  action,  trace  characters  with  the  wire  on  the  paper. 
The  discharge  decomposes  the  potassium  iodide,  as  shown  by  the  blue 
mark.     This  blue  mark  is  due  to  the  action  of  the  iodine  on  the 
starch. 

If  the  current  from  the  secondary  of  an  induction  coil  be  passed 
through  air  in  a  sealed  tube,  the  nitrogen  and  oxygen  will  combine  to 
form  nitrous  acid.  This  is  the  basis  of  some  of  the  commercial 
methods  of  manufacturing  nitrogen  compounds  from  the  nitrogen  of 
the  air. 

4.  Heating  Effects.  —  Figure  433  shows  the  plan  of  the  "  electric 
bomb."     It  is  usually  made  of  wood.     Fill  the  hole  with  gun  powder 


410 


ELECTEOMAGNETIC  INDUCTION 


FIGURE  433.  —  ELECTRIC  BOMB. 


as  far  up  as  the  brass  rods  and  close  the  mouth  with  a  wooden  ball. 

Connect  the  rods  to  the  poles  of  the  induction  coil.     The  sparks  will 

ignite  the  powder  and  the  ball  will 
be  projected  across  the  room. 

The  heating  effect  of  the  current 
in  the  secondary  of  a  large  induction 
coil  may  be  shown  by  stretching 
between  its  poles  a  very  thin  iron 
wire  with  a  small  gap  in  it.  The 
discharge  will  melt  the  part  con- 
nected to  the  negative  pole  of  the 
coil,  while  the  other  part  will  re- 
main below  the  temperature  of 
ignition. 

506.  Discharges  in  Partial 
Vacua.  —  Place  a  vase  of  uranium 
glass  on  the  table  of  the  air  pump, 

under  a  bell  jar  provided  with  a  brass  sliding  rod  passing  air-tight 

through  the  cap  at  the  top  (Fig.  434).     Connect  the  rod  and  the  air 

pump  table  to  the  terminals  of  the  induction  coil.     When  the  air  is 

exhausted  a  beautiful  play  of  light  will  fill  the 

bell  jar.     The  display  will  be  more  beautiful  if 

the    vase   is   lined   part  way  up  with   tin-foil. 

This  experiment  is  known  as  Gassiol's  cascade. 

The  experiment   may   be  varied  by   admitting 

other  gases  and  exhausting  again.     The  aspect 

of  the  colored  light  will  be  entirely  changed. 

The  best  effects  are  obtained  with 
discharges  from  the  secondary  of  an  in- 
duction coil  in  glass  tubes  when  the 
exhaustion  is  carried  to  a  pressure  of 
about  2  ram.  of  mercury,  and  the  tubes 
are  permanently  sealed.  Platinum  elec- 
trodes are  melted  into  the  glass  at  the  two  ends.  Such 
tubes  are  known  as  Geissler  tubes.  They  are  made  in 
a  great  variety  of  forms  (Fig.  435),  and  the  luminous 
effects  are  more  intense  in  the  narrow  connecting  tubes 


FIGURE  434.  —  GAS- 
SIOT'S  CASCADE. 


THE  DISCHARGE  INTERMITTENT 


411 


FIGURE  435.  —  GEISSLER  TUBES. 


Stratifications    have    been 


than  in  the  large  bulbs  at  the  ends.  The  colors  are  de- 
termined by  the  nature  of  the  residual  gas.  Hydrogen 
glows  with  a  brilliant  crimson;  the  vapor  of  water  gives 
the  same  color,  indicating 
that  the  vapor  is  disso- 
ciated by  the  discharge. 
An  examination  of  this 
glow  by  the  spectroscope 
gives  the  characteristic 
lines  of  the  gas  in  the  tube. 
Geissler  tubes  often  ex- 
hibit stratifications,  which 
consist  of  portions  of 
greater  brightness  sepa- 
rated by  darker  intervals, 
produced  throughout  a  tube  50  feet  long.  These  stratifi- 
cations or  striae  present  an  unstable  flickering  motion,  re- 
sembling that  sometimes  observed  during  auroral  displays. 

507.  The  Discharge  Intermittent.  —  On  a  disk  of  white  card- 
board about  20  cm.  in  diameter  paste  disks  of  -black  paper  2  cm.  in 
diameter  (Fig.  436).  Rotate  the  disk 
rapidly  by  means  of  a  whirling  table  or 
an  electric  motor  and  illuminate  it  by  a 
Geissler  tube  in  a  dark  room.  The  black 
spots  will  be  sharp  in  outline  because 
each  flash  is  nearly  instantaneous;  and 
the  spots  in  the  different  circles  will 
either  stand  still,  rotate  forward,  or  rotate 
backward.  If  in  the  brief  interval  be- 
tween the  flashes  the  disk  rotates  through 
an  angle  equal  to  that  between  the  spots 
in  one  of  the  circles,  the  spots  will  appear 
to  stand  still;  if  it  rotates  through  a 
slightly  greater  angle,  the  spots  will  appear  to  move  slowly  forward ; 
if  through  a  smaller  angle,  they  will  appear  to  move  slowly  backward. 


FIGURE  436.  —  DISK  FOR  IN- 
TERMITTENT ILLUMINATION. 


412 


ELECTROMAGNETIC  INDUCTION 


Mount  a  Geissler  tube  on  a  frame  attached  to  the  axle  of  a  small 
electric  motor  (Fig.  437).  Illuminate  the  tube  by  an  induction  coil 
while  it  rotates.  Star-shaped  figures  will 
be  seen,  consisting  of  a  number  of  images 
of  the  tube,  the  number  depending  on  the 
speed  of  the  motor  as  compared  with  the 
period  of  vibration  of  the  circuit  breaker. 

508.  Cathode  Rays.  —  When  the 
gas  pressure  in  a  tube  is  reduced 
below  about  a  millionth  of  an  atmos- 
phere, the  character  of  the  discharge 
is  much  altered.  The  positive 
column  of  light  extending  out  from 
the  anode  gradually  disappears,  and 
the  sides  of  the  tube  glow  with 
brilliant  phosphorescence.  With 
English  glass  the  glow  is  blue  ;  with 
German  glass  it  is  a  soft  emerald. 

The  luminosity  of  the  glass  is  produced  by  a  radiation  in 

straight  lines  from  the  cathode  of  the  tube ;   this  radiation 

is  known  as  cathode  rays.     They  were  first  studied  by 

Sir  William    Crookes, 

and  the  tubes  for  the 

purpose    are   called 

Crookes  tubes. 


FIGURE    437.  —  ROTATION 
OF  GEISSLER  TUBE. 


Many  other  substances 
besides  glass  are  caused  to 
glow  by  the  impact  of  cath- 
ode rays  (Fig.  438),  such 
as  ruby,  diamond,  and  va- 
rious sulphides.  The  color 
of  the  glow  depends  on  the 
substance. 

Cathode  rays  have  a  mechanical  effect.    In  fact  they  consist  of 
electrons  (§  518)  moving  with  yery  high  velocity  approaching  that 


FIGURE  438.  —  FLUORESCENCE  BY  CATHODE 
RAYS. 


Sir  William  Crookes,  a  dis- 
tinguished English  chemist, 
was  born  in  1832.  In  1873 
he  began  a  series  of  investi- 
gations on  the  properties  of 
high  vacua.  While  engaged 
in  this  work  he  invented  the 
radiometer,  developed  the 
Crookes  tubes,  and  dis- 
covered what  he  called  "ra- 
diant matter."  His  investi- 
gations led  him  very  close  to 
the  discoveries  of  Rbntgen. 
He  edited  the  Quarterly  Jour- 
nal of  Science  from  1864  until 
his  death 'in  1919. 


Wilhelm  Konrad  Rontgen 
was  born  in  1845.  It  was 
at  Wiirzburg,  Germany,  in 
1895,  that  he  discovered 
while  passing  electric  charges 
through  a  Crookes  tube,  that 
a  certain  kind  of  radiation 
was  emitted  capable  of  pass- 
ing through  many  substances 
known  to  be  opaque  to  light. 
The  nature  of  these  rays 
being  unknown,  he  called 
them  '  •  X-rays."  They  differ 
from  the  cathode  rays  dis- 
covered by  Crookes,  in  that 
they  affect  a  sensitized  photo- 
graphic plate. 


CATHODE  BATS 


413 


of  light.  When  they  strike 
a  target,  their  motion  is 
arrested  and  their  energy 

of  motion  is  largely  trans- 

,        .'  FIGURE  439.  —  RAILWAY  TUBE. 

ferred  to  the  target.     The 

light  paddle  wheel  in  Figure  439  runs  smoothly  on  glass  rails.     It  may 


FIGURE  440.  —  MAGNETIC  DEFLECTION  OF  CATHODE  RAYS. 

be  made  to  traverse  the  tube  in  either  direction  by  projecting  elec- 
trons from  the  cathode  against  the 
paddles  on  top.  When  the  cathode 
is  changed  from  one  end  to  the 
other  by  reversing  the  current  in 
the  induction  coil,  the  little  wheel 
stops  promptly  and  reverses  its  di- 
rection. Its  paddles  are  driven  as 
if  by  a  blast  from  the  cathode  disk. 
Cathode  rays,  unlike  rays  of  light, 
are  deflected  by  a  magnet,  and  when 
once  deflected  they  do  not  regain 
their  former  direction  (Fig.  440). 
Cathode  rays  proceed  in  straight 
lines,  except  as  they  are  deflected 
by  a  magnet  or  by  mutual  repul- 
sion. A  screen  placed  across  their 
path  interrupts  them  and  casts  a 
shadow  on  the  walls  of  the  tube. 

When  the  cathode  is  made  in  the 
form  of  a  concave  cup,  the  rays  are 
FIGURE  441.  —  Focus  TUBE.          brought  to  a  focus  near  its  center  of 


414 


ELECTROMAGNETIC  INDUCTION 


curvature;  platinum  foil  placed  at  this  focus  is  raised  to  bright 
incandescence  and  may  be  fused  (Fig.  441).  Glass  on  which  an 
energetic  cathode  stream  falls  may  be  heated  to  the  point  of  fusion. 

It  has  been  conclusively  shown  that  cathode  rays  carry 
negative  charges  of  electricity.  Hence  the  mutual  repul- 
sion exerted  on  each  other  by  two  parallel  cathode  streams. 
509.  Roentgen  Rays.  —  The  rays  of  radiant  matter,  as 
Crookes  called  it,  emanating  from  the  cathode,  give  rise  to 
another  kind  of  rays  when  they  strike  the  walls  of  the 
tube,  or  a  piece  of  platinum  placed  in  their  path.  These 
last  rays,  to  which  Roentgen,  their  discoverer,  gave  the 

name  of  "  X-rays" 
can  pass  through 
glass,  and  so  get 
out  of  the  tube. 
They  also  pass 
through  wood, 
paper,  flesh,  and 

FIGURE  442. -ROENTGEN  TUBE.  man7     other     sub' 

stances  opaque  to 

light.  They  are  stopped  by  bones,  metals  (except  in  very 
thin  sheets),  and  by  some  other  substances.  Roentgen 
discovered  that  they  affect  a  photographic  plate  like  light. 
Hence,  photographs  can  be  taken  of  objects  which  are 
entirely  invisible  to  the  eye,  such  as  the  bones  in  a  living 
body,  or  bullets  embedded  in  the  flesh. 

A  Crookes  tube  adapted  to  the  production  of  Roentgen 
rays  (Fig.  442)  has  a  concave  cathode  K,  and  at  its  focus 
an  inclined  piece  of  platinum  A,  which  serves  as  the  anode. 
The  X-rays  originate  at  A  and  issue  from  the  side  of  the 
tube. 

510.  X-Ray  Pictures.  —  The  penetrating  power  of  Roentgen  rays 
depends  largely  on  the  pressure  within  the  tube.  With  high  exhaus- 


THE  FLUOROSCOPE 


415 


With  somewhat  lower 


tion  the  rays  have  high  penetrating  power  and  are  then  known  as 
"hard  rays."  Hard  rays  can  readily  penetrate  several  centimeters  of 
wood,  and  even  a  few  millimeters  of  lead. 

exhaustion,    the   rays   are      . 

less  penetrating  and  are 
then  known  as  "soft  rays." 
The  possibility  of  X-ray 
photographs  depends  on 
the  variation  in  the  pene- 
trability of  different  sub- 
stances for  X-rays.  Thus, 
the  bones  of  the  body  ab- 
sorb Roentgen  rays  more 
than  the  flesh,  or  are  less 
penetrable  by  them. 
Hence  fewer  rays  traverse 
them.  Since  Roentgen 
rays  cannot  be  focused,  all 
photographs  takenby  them 
are  only  shadow  pictures. 
A  Roentgen  photograph  of 
a  gloved  hand  is  shown  in 
Figure  443.  The  ring  on 
the  little  finger,  and  the 
cuff  studs  are  conspicu- 
ous. The  flesh  is  scarcely 
visible  because  of  the  high 

penetrating  power  of  the  rays  used.     The  photographic  plate  for  the 
purpose  is  inclosed  in  an  ordinary  plate  holder  and  the  hand  is  laid 

on  the  holder  next  to  the  sensitized  side. 

* 

511.  The  Fluoroscope.  —  Soon  after  the  discovery  of 
X-rays  it  was  found  that  certain  fluorescent  substances, 
like  platino-barium-cyanide,  and  calcium  tungstate,  be- 
come luminous  under  the  action  of  X-ra}^s.  This  fact 
has  been  turned  to  account  in  the  construction  of  &fluoro- 
scope  (Fig.  444),  by  means  of  which  shadow  pictures  of 
concealed  objects  become  visible.  An  opaque  screen  is 


FIGURE  443.  —  X-RAY  PICTURE. 


416  ELECTROMAGNETIC  INDUCTION 

covered  on  one  side  with  the  fluorescent  substance ;  this 
screen  fits  into  the  larger  end  of  a  box  blackened  inside, 

and  having  at  the  other  end 
an  opening  adapted  to  fit 
closely  around  the  eyes,  so 
as  to  exclude  all  outside 
light.  When  an  object,  such 
as  the  hand,  is  held  against 
the  fluorescent  screen  and 
the  fluoroscope  is  turned 
FIGURE  444.  —  FLUOROSCOPE.  toward  the  Roentgen  tube, 

the  bones  are  plainly  visible 

as  darker  objects  than  the  flesh  because  they  are  more 
opaque  to  X-rays.  The  beating  heart  may  be  made  visible 
in  a  similar  manner. 

IV.     RADIOACTIVITY  AND  ELECTRONS 

512.  Radioactivity.  —  Wrap  a  photographic  plate  in  black  paper. 
Flatten  a  Welsbach  mantle  and  lay  it  on  the  paper  next  to  the  film 
side  of  the  plate.     Place  the  whole  in  a  light-tight  box  for  about  a 
week.     If  the  plate  be  now  developed,  a  photographic  picture  of  the 
itiantle  will  appear  on*it. 

The  mantle  contains  the  rare  metal  thorium.  This 
,met&l  'po^jsesses  tKte  property-  of  emittiri££  all  the  time 
radiations  that  act  like .  A-rays  oh  a  ^hqto^aphic  .plate. 
Substances  having'this  property  are  known  as  radioactive. 
The  principal  ones  are  uranium,  polonium,  actinium,  tho- 
rium, radium,  and  their  compounds. 

513.  Discovery  of  Radioactivity.  — The  activity  of  X-rays 
in  producing  photographic  changes  led  directly  to  the  dis- 
covery of  the  radioactivity  of  uranium  by  Becquerel  in 
1896.     He  found  that  uranium  salts  give  off  spontaneously 
radiations  capable  of  passing  through  black  paper  and  thin 


THREE  KINDS   OF  RADIUM  RATS 


417 


sheets  of  aluminum  foil,  and  that  they  affect  photographic 
plates  as  X-rays  do.  These  radiations  are  not  modified  in 
any  way  by  the  most  drastic  treatment  of  the  uranium, 
whether  by  heat  or  cold  or  other  physical  changes. 

514.  Radium.  —  Two  years  after  Becquerel's  discovery 
Madame  Curie  found  in  pitchblende  (an  impure  oxide  of 
uranium)  a  constituent  much  more  highly  radioactive  than 
uranium  itself.     She  succeeded  by  chemical  means  in  ex- 
tracting this  remarkable  substance  from  pitchblende  and 
named  it  radium. 

Radium  is  a  million  times  more  radioactive  than  ura- 
nium. Although  widely  distributed,  the  total  quantity  of 
radium  in  the  earth  is  undoubtedly  small.  It  takes  150 
tons  of  pitchblende  to  furnish  one  ounce  of  radium.  It  is 
a  hard  white  metal,  resembling  barium.  It  is  very  un- 
stable and  is  usually  prepared  and  used  as  a  chloride  or  a 
bromide.  Its  radiations  excite  strong  fluorescence  in 
several  substances,  notably  zinc  sulphate,  diamond,  and 
ruby;  and  they  produce  on  the 
human  body  sores  difficult  to  heal. 

515.  Three  Kinds  of  Radium  Rays.  — 
Rutherford  has   shown  that  radium 
emits  three  kinds  of  "rays,"  which 
can  be  separated  by  means  of  a  strong 
magnetic  field.     Their  difference  in 
behavior  in  a  magnetic  field  is  illus- 
trated in  Figure  445.     The  radium  is 
placed  at  the  bottom  of  a  small  hole 
in  a  block  of  lead,  so  that  only  a  thin 
pencil  of  rays  escapes  in  a  vertical 

direction.  A  strong  magnetic  field  is  applied  so  that  the 
lines  of  force  run  away  from  the  observer.  The  radiations 
are  then  separated  into  three  kinds,  known  as  alpha,  beta, 


FIGURE    445.  —  ALPHA, 
BETA,  AND  GAMMA  RAYS. 


418  ELECTROMAGNETIC  INDUCTION 

and  gamma  rays.  The  alpha  rays  are  slightly  deflected 
to  the  left,  the  beta  rays  strongly  to  the  right,  while  the 
gamma  rays  are  not  affected  in  the  least.  The  fact  that 
the  alpha  and  beta  rays  suffer  deviations  in  opposite  direc- 
tions shows  not  only  that  they  are  charged  particles,  but 
that  they  are  oppositely  charged,  the  former  positively 
and  the  latter  negatively. 

The  alpha  rays  are  positively  charged  particles  emitted 
with  an  average  velocity  about  one-fifteenth  the  speed  of 
light.  They  have  little  penetrating  power  and  are  ab- 
sorbed by  a  sheet  of  ordinary  writing  paper. 

The  beta  rays  are  negatively  electrified,  highly  penetra- 
tive, and  identical  in  nature  with  cathode  rays  (§  508). 
They  travel  with  an  average  speed  from  about  one-half 
down  to  about  one-tenth  that  of  light. 

The  gamma  rays  are  of  very  high  penetrating  power,  they 
travel  with  the  velocity  of  light,  and  appear  to  be  identical 
with  X-rays.  They  show  no  trace  of  electrification. 

516.  Radium  a  Product  of  Disintegration. — Uranium  has 
the  highest  atomic  weight  of  any  known  substance,  and  it 
is  always  associated  in  nature  with  other  radioactive  sub- 
stances. This  association  suggested  that  the  other  ra'dio- 
active  substances  are  derived  from  uranium  by  its  dis- 
integration, or  loss  of  particles  with  reduction  of  atomic 
weight.  Such  has  been  found  to  be  the  case.  Uranium 
is  the  parent  of  ionium,  and  ionium  is  the  parent  of  radium. 
Radium  is  thus  a  product  of  disintegration. 

Further,  the  radium  atom  disintegrates  with  the  expul- 
sion of  an  alpha  particle  ;  and  the  alpha  particle,  after  losing 
its  positive  charge,  becomes  an  atom  of  helium.  Thus  a 
known  element  is  produced  during  the  transformation  of 
radioactive  matter.  All  alpha  particles  from  whatever 
source  consist  of  helium  atoms  carrying  positive  charges. 


Madame  Marie  Sklodowska  Curie  was  born  in  Warsaw  in 
1867.  She  imbibed  the  spirit  of  scientific  research  from  her 
father,  a  distinguished  physicist  and  chemist.  In  1895  she  mar- 
ried Professor  Curie  of  the  University  of  Paris.  Three  times  she 
has  been  awarded  the  Gegner  prize  by  the  French  Academy  for 
her  valuable  contributions  to  the  world's  knowledge  of  the  mag- 
netic properties  of  iron  and  steel  and  for  her  discoveries  in  radio- 
activity. In  1903  and  again  in  1911  the  Nobel  prize  was  awarded 
her.  In  January  of  1911  she  failed  only  by  two  votes  of  election 
to  membership  in  the  French  Academy  of  Sciences,  being  de- 
feated by  Branley,  the  inventor  of  the  coherer  used  in  the  Mar- 
coni system  of  wireless  telegraphy. 


Sir  Joseph  John  Thomson  was  born  near  Manchester,  Eng- 
land, in  1856.  He  received  his  early  training  at  Owens  College, 
and  acquired  there  some  knowledge  of  experimental  work  in  the 
laboratory  of  Balfour  Stewart.  At  the  age  of  twenty-seven  he 
was  appointed  to  the  Cavendish  professorship  at  the  University  of 
Cambridge,  a  position  made  famous  by  Maxwell  and  Rayleigh. 
The  wisdom  of  the  appointment  was  soon  proved;  for  shortly 
after,  Thomson  began  a  series  of  experiments  on  the  conduction 
of  electricity  through  gases,  culminating  in  the  discovery  of  the 
"electron,"  out  of  which  has  developed  the  electron  theory  of 
matter. 


ELECTRONS  419 

I 

Evidence  derived  from  the  study  of  uranium  minerals 
makes  it  almost  certain  that  the  final  product  of  the  dis- 
integration of  uranium  is  lead. 

517.  Heat  Generated  by  Radium. — The  salts  of   radium 
exhibit  an  altogether  new  and  remarkable  property ;   they 
are  always  maintained  at  a  temperature  several  degrees 
higher  than  that  of  the  surrounding  air.     They  are  thus 
always  radiating  heat  and  giving  out  energy.     A  gram  of 
pure  radium  would  emit  heat  at  the  rate  of  from  100  to 
130  calories  per  hour.     It  has  been  estimated  that  before 
a  gram  of  radium  is  exhausted  it  would  emit  enough  heat 
to  melt  a  gram  of  ice  every  hour  for  1000  years.     Also, 
that  the  energy  of  radium  is  a  million  and  a  half  times 
greater  than  that  of  an  equal  mass  of  coal. 

518.  Electrons.  —  Sir  William  Crookes,  at  the  time  of  his 
discovery  of  the  cathode  discharge,  regarded  it  as  matter 
in  a  radiant  state.     Later  it  was  demonstrated  that  the 
cathode  discharge  carries  negative  electricity.     Still  later, 
by  a  series  of  brilliant  experiments,  Sir  J.  J.   Thomson 
proved  that  cathode  "rays"  consist  of  streams  of  negatively 
electrified  particles,  now  called  electrons.     The  mass  of  an 
electron  is  only  about  y^VlF  °^  the  mass  °f  the  hydrogen 
atom.     Moreover,  he  measured  their  speed  in  a  vacuum 
and  found  it  to  have  the  enormous  value  of  about  50,000 
miles  per  second. 

The  electron  is  invariable  in  magnitude,  and  is  said  to 
be  "  the  atom  of  electricity,"  that  is,  the  smallest  quantity 
of  electricity  that  can  be  transferred  from  one  atom  of 
matter  to  another.  It  is  the  smallest  quantity  that  exists 
in  a  separate  state. 

The  beta  rays  spontaneously  emitted  by  radium  and  other 
radioactive  matter  have  now  been  identified  with  the  elec- 
trons of  a  Crookes  tube.  There  is  good  evidence  also  that 


420  ELECTROMAGNETIC  INDUCTION 

the  electron  is  identical  with  the  single  atomic  charge  of 
a  negative  ion  in  electrolysis.  If  positive  electricity  is 
atomic,  its  atom  is  several  thousands  of  times  greater  than 
the  atomic  quantity  of  negative  electricity. 

Electrons  enter  into  the  composition  of  all  matter.  An 
electric  current  is  supposed  to  be  a  stream  of  electrons 
flowing  under  electric  pressure  through  a  conductor  from 
negative  to  positive. 


CHAPTER   XIV 

DYNAMO-ELECTRIC  MACHINERY 
I.     DIRECT  CURRENT  MACHINES 

519.  A  Dynamo-Electric  Generator  is  a  machine  to  convert 
mechanical  energy  into  the  energy  of  currents  of  electric- 
ity.    It  is  a  direct  outgrowth  of  the  brilliant  discoveries 
of  Faraday  about  induced  electromotive  forces  and  currents 
in  1831.     It  is  an  essential  part  of  every  system,  steam  or 
hydro-electric,  for  electric  lighting,  the  transmission  of 
electric  power,  electric  railways,  electric  locomotives,  elec- 
tric train  lighting,  the  charging  of  storage  batteries,  electric 
smelting,  electrolytic  refinement  of  metals,  and  for  every 
other  purpose  to  which  large  electric  currents  are  applied. 

520.  Essential  Parts  of  a  Dynamo-Electric  Machine.  —  Every 
dynamo-electric  machine  has  three  essential  parts:    1.   The 
field  magnet  to  produce  a  powerful  magnetic  field.     2.  The 
armature,  a  system  of  conductors  wound  on  an  iron  core, 
and  revolving  in  the  magnetic  field  in  such  a  manner  that 
the  magnetic  flux  through  these  conductors   varies  con- 
tinuously.    3.  The  commutator,  or  the  collecting  rings  and 
the  brushes,  by  means  of  which  the  machine  is  connected 
to  the  external  circuit.     If  the  magnetic  field  is  produced 
by  a  permanent  magnet,  the  machine  is  called  a  magneto, 
such  as  is  used  in  an  automobile  for  ignition ;   if  by  an 
electromagnet,  the  machine  is  a  dynamo,  which  is  used  in 
electric  lighting  stations,  and  for  all  other  purposes  requir- 
ing large  currents  generated  by  high  power.     Both  are 
often  called  generators. 

421 


422  DYNAMO-ELECTRIC  MACHINERY 

521.  Ideal  Simple  Dynamo.  —  For  the  purpose  of  simpli- 
fying what  goes  on  in  the  revolving  coils  of  a  generator, 
let  us  consider  a  single  loop  of  wire  revolving  between  the 
poles  of  a  magnet  (Fig.  446)  in  the  direction  of  the  arrow 

and  around  a  horizontal 
axis.  The  light  lines 
indicate  the  magnet  fluy 
running  across  from  N 
to  S.  In  the  position  of 
the  loop  drawn  in  full 

lines   it   incloses   the 

FIGURE  446.  —  IDEAL  SIMPLE  DYNAMO. 

largest  possible  magnetic 

flux  or  lines  of  force,  but  as  the  flux  inclosed  by  the  coil 
is  not  changing,  the  induced  E.M.F.  is  zero. 

When  it  has  rotated  forward  a  quarter  of  a  turn,  its 
plane  will  be  parallel  to  the  magnetic  flux,  and  no  lines 
of  force  will  then  pass  through  it.  During  this  quarter 
turn  the  decrease  in  the  magnetic  flux,  threading  through 
the  loop,  generates  a  direct  E.M.F. ;  and  if  the  rotation 
is  uniform,  the  rate  of  decrease  of  flux  through  the  loop 
increases  all  the  way  from  the  first  position  to  the  one 
shown  by  the  dotted  lines,  where  it  is  a  maximum.  The 
arrows  on  the  loop  show  the  direction  of  the  E.M.F. 

During  the  next  quarter  turn  there  is  an  increase  of 
flux  through  the  loop,  but  it  runs  through  the  loop  in 
the  opposite  direction  because  the  loop  has  turned  over ; 
this  is  equivalent  to  a  continuous  decrease  in  the  original 
direction,  and  therefore  the  direction  of  the  induced 
E.M.F.  around  the  loop  remains  the  same  for  the  entire 
half  turn;  the  E.M.F.  again  becomes  zero  when  the 
half  turn  is  completed. 

After  the  half  turn,  the  conditions  are  all  reversed  and 
the  E.  M.  F.  is  directed  the  other  way  around  the  loop. 


THE  COMMUTATOR 


423 


/ 

s 

x 

\ 

/ 

<•* 

/ 

f 

\^ 

. 

7 

/ 

\ 

/ 

y 

0' 

u 

, 

2 

0" 

z 

0" 

uo 

\ 

w 

/ 

s 

^ 

^ 

/ 

If  there  are  several  turns  in  the  coil,  the  E.  M.  F.  reverses 
in  all  of  them  twice  every  revolution. 

The  curve  of  Figure  447  shows  by  its  ordinates  the  suc- 
cessive relative  values  of  tho  induced  electromotive  forces 
when  the  coil  rotates 
with  uniform  speed.  If 
the  coil  is  part  of  a 
closed  circuit,  the  cur- 
rent through  it  reverses 
twice  every  revolution, 
that  is,  it  is  an  alternat- 

FIGURE  447.  —  CURVE  OF  E.  M.  F.'s. 
ing  current. 

522.  The  Commutator.  —  When  it  is  desired  to  convert 
the  alternating  currents  flowing  "in  the  armature  into  a 
current  in  one  direction  through  the  external  circuit,  a 
special  device  called  a  commutator  is  employed.  For  a 
single  coil  in  the  armature,  the  comm  utator  consists  of  two 
parts  only.  It  is  a  split  tube  with  the  two  halves,  a  and  5, 
insulated  from  each  other  and  from  the  shaft  8  on  which 
they  are  mounted  (Fig.  448).  The  two  ends  of  the  coil 

(not  shown)  are  connected 
with  the  two  halves  of  the 
tube. 

Two  brushes,  with  which 
the  external  circuit  L  L  is 
connected,  bear  on  the  com- 
mutator, and  they  are  so 
placed  that  they  exchange 
contact  with  the  two  commu- 
tator segments  at  the  same  time  that  the  current  reverses 
in  the  coil.  In  .this  way  one  of  the  brushes  is  always 
positive  and  the  other  negative,  and  the  current  flows  in 
the  external  circuit  from  the  positive  brush  back  to  the 


FIGURE  448.  —  TWO-PART  COMMU- 
TATOR. 


424 


DYNAMO-ELECTRIC  MACHINERY 


/ 

/" 

vs 

\ 

/ 

S 

X 

\ 

/ 

^ 

\ 

s 

A 

\ 

/ 

/ 

\ 

/ 

\ 

/ 

« 

0° 

1 

(}' 

'i 

W 

1 

0" 

90 

FIGURE  449.  —  RECTIFIED  E.  M.  F.'s. 


negative,  and  thence  through  the  armature  to  the  positive 
again ;  but  with  a  single  coil  the  current  is  pulsating,  or 

falls  to  zero  twice  every 
revolution  (Fig.  449). 

523.  The  Gramme  Ring. 
—  The  use  of  a  commu- 
tator with  more  than 
two  parts  is  conven- 
iently illustrated  in 
connection  with  the 
Grramme  ring.  This  ar- 
mature has  gone  out  of  practical  use,  but  it  is  useful  here 
because  it  can  be  understood  from  a  simple  diagram ;  and 
fundamentally  its  action  is  the  same  as  that  of  the  com- 
mon drum  type. 

The  Gramme  ring  has  a  core  made  either  of  iron  wire, 
or  of  thin  disks  at  right  angles  to  the  axis  of  rotation. 
The  iron  is  divided  for  the  purpose  of  preventing  induc- 
tion or  eddy  currents  in  it,  which  waste  energy.  The  re- 
lation of  the  several  parts  of  the  machine  is  illustrated  by 
Figure  450.  A  number  of  coils  are  wound  in  one  direction 
and  are  all  joined  in  series.  The  coils  must  be  grouped 
symmetrically  so  that  some 
of  them  are  always  active, 
thus  generating  a  continuous 
current.  Each  junction  be- 
tween coils  is  connected  with 
a  commutator  bar.  Most  of 
the  magnetic  flux  passes 
through  the  iron  ring  from  FlGURE  45°—  THE  GRAMME  Rma 
the  north  pole  side  to  the  south  pole ;  bence,  when  a  coil 
is  in  the  highest  position  in  the  figure,  the  maximum  flux 
passes  through  it  i  as  the  ring  rotates,  the  flux  through  the 


THE  FIELD  MAGNET  425 

coil  decreases,  and  after  a  quarter  of  a  revolution  there  is 
no  flux  through  it.  The  current  through  each  coil  reverses 
twice  during  each  revolution,  exactly  as  in  the  case  of  the 
single  loop.  No  current  flows  entirely  around  the  arma- 
ture, because  the  JH.M.F.  generated  in  one  coil  at  any  in- 
stant is  exactly  counterbalanced  by  the  E.M.F.  generated  in 
the  coil  opposite.  But  when  the  external  circuit  connect- 
ing the  brushes  is  closed,  a  current  flows  up  on  both  sides 
of  the  armature.  The  current  has  then  two  paths  through 
the  armature,  and  one  brush  is  constantly  positive  and  the 
other  negative.  The  current  is  therefore  direct  and  fairly 
steady. 

524.  The  Drum  Armature.  —  This  very 
useful  form  of  armature  is  in  universal 
use  for  direct  current  (D.  C.)  genera- 
tors.    The  core  is  made  up  of  thin  iron 
disks  stamped    out  with  teeth  around 
the  periphery  (Fig.  451).     When  these 

are   assembled  on  the  shaft,  the  slots        FIGURE   451.  — 

-  TOOTHED  DISK. 

form  grooves  in  which  are  placed  the 

armature  windings.  All  the  coils  in  the  armature  may  be 
joined  in  series,  and  the  junctions  between  them  are  con- 
nected to  the  commutator  bars,  as  in  the  Gramme  ring. 

525.  The  Field  Magnet.  —  The  magnetic  field  in  dynamos 
is  produced  by  a  large  electromagnet  excited  by  the  cur- 
rent flowing  from  the  armature  ,  this  current  is  led,  either 
wholly  or  in  part,  around  the  field-magnet  cores.     When 
the  entire  current  is  carried  around  the  coils  of  the  field 
magnet,  the   dynamo   is  said   to   be    series  wound  (Fig. 
452  a).     When  the  field  magnet   is   excited  by  coils  of 
many  turns  of  fine  wire  connected  as  a  shunt  to  the  exter- 
nal circuit,  the  dynamo  is  said  to  be  shunt  wound  (Fig. 
452  6).     A  combination  of  these  two  methods  of  exciting 


426 


DYNAMO-ELECTRIC  MACHINERY 


the  field  magnet  is  called  compound  winding  (Fig.  452  <?). 
The  residual  magnetism  remaining  in  the  cores  is  suffi- 
cient to  start  the  machine.  The  current  thus  produced 


FIGURE  452.  —  FIELD  MAGNET  WINDINGS. 

increases  the  magnetic  flux  through  the  armature  and  so 
increases  the  E.M.F. 

526.  The  Modern  Generator.  —  Large  modern  D.  C.  gen- 
erators are  multipolar,  with  four,  six,  or  eight,  or  more 
poles.     The  larger  number  of  poles  reduces  the  rate  of 
rotation  of  the  armature.     In  the  field  magnet  shown  in 
the  half  tone  on  the  opposite  page  there  are  sixteen  poles, 
north  poles  and  south  poles  alternating  around  the  ring. 
The  armature  is  wound   in  loops  which   reach  across  a 
chord  nearly  equal  to  the  pitch  of  the  poles,  so  that  when 
one  side  of  a  loop  is  passing  a  north  pole,  the  opposite 
side  is  passing  an  adjacent  south  pole.     In  a  simple  drum 
armature  there  are   as   many  brushes   as  there  are  field 
poles,  and  there  are  the  same  number  of  parallel  paths  or 
circuits  through  the  windings  as  there  are  brushes.     An 
engine  type  of  multipolar  drum  armature  is  shown  in  the 
illustration  on  the  opposite  page. 

527.  The  Electric  Motor.  —  The  electric  motor  is  a  machine 
for  the  conversion  of  the  energy  of  electric  currents  into 
mechanical  power. 


THE  ELECTRIC  MOTOR 


427 


In  the  electric  automobile  and  in  the  electric  starter  for  gasoline 
machines  the  motor  is  driven  by  currents  from  a  storage  battery.  In 
the  electric  street  car  it  derives  its  current  and  power  from  a  trolley, 
a  third  rail,  or  from  conductors  fixed  in  a  slotted  conduit  under  the 
pavement,  all  of  them  leading  back  to  a  power  house  or  a  substation. 
The  electric  motor  is  extensively  used  for  small  power  as  well  as  for 
large  units.  Witness  the  use  of  electric  fans,  electric  coffee  grinders, 
sewing  machine  motors,  and  electrically  driven  bellows  for  pipe  organs 
on  one  hand,  and  on  the  other  the  electric  drive  for  large  fans  to  ven- 
tilate mines  and  buildings,  electric  elevators,  and  electrically  driven 
mills  and  factories. 

An  electric  motor  for  direct  currents  is  constructed  in 
the  same  manner  as  a  generator.  In  fact,  any  direct  cur- 
rent generator  may  be  used  as  a  motor.  A  study  of  the 
magnetic  field  resulting  from  the.  interaction  of  the  field 
due  to  the  field  magnet  and  that  of  a  single  loop  carrying 
an  electric  current  will  make 
it  clear  that  such  a  loop  has 
a  tendency  to  rotate. 

Figure  453  was  made  from 
a  photograph  of  the  field 
shown  by  fine  iron  filings 
between  unlike  poles.  This 
field  is  distorted  by  a  current 
through  a  loop  of  wire,  which 
came  up  through  the  hole  on 
the  right  in  the  glass  plate  and  went  down  through  the  other. 
Many  of  the  lines  of  force  are  threaded  through  the  wire 
loop  instead  of  running  directly  across  from  one  magnetic 
pole  to  the  other.  Now  the  lines  of  magnetic  force  are 
under  tension  and  tend  to  straighten  out ;  this  straight- 
ening brings  a  magnetic  stress  to  bear  on  the  loop  carrying 
the  current  and  tends  to  turn  it  counter-clockwise  in  the 
case  shown  in  the  figure. 


FIGURE  453.  —  MAGNETIC  FIELD 
DISTORTED  BY  CURRENT. 


428  DYNAMO-ELECTRIC  MACHINERY 

If  the  loop  be  allowed  to  rotate  in  the  direction  of  this 
magnetic  effort  between  the  field  and  the  loop,  the  loop 
will  become  the  armature  of  a  motor  and  work  will  be 
done  by  the  machine  at  the  expense  of  the  energy  of  the 
current  flowing  through  it.  If,  however,  the  loop  be 
forcibly  rotated  clockwise  by  mechanical  means,  it  will 
turn  against  the  magnetic  effort  acting  on  it,  and  work 
will  be  done  against  the  resistance  of  this  magnetic 
drag.  The  loop  will  then  be  the  armature  wire  of  a 
generator. 

528.  Forms  of  D.  C.  Motors.  —  Since  any  D.  C.  generator 
will  run  as  a  motor,  we  find  D.  C.  motors  either  series  or 
shunt  wound  according  to  the  .service  for  which  they  are 
designed.  Series  wound  motors  are  used  on  street  cars  and 
electric  automobiles,  where  the  service  requires  variable 
speed.  .  Shunt  wound  motors  are  used  to  run  machinery  in 
shops  and  factories,  where  constant  speed  is  desirable. 
High  speed  motors  are  usually  bipolar ;  motors  for  slow 
speed  service  have  multipolar  fields. 

The  torque,  or  turning  moment,  of  an  electric  motor 
depends  both  upon  the  strength  of  the  magnetic  field 
and  the  current  through  the  armature.  In  a  shunt 
wound  motor  the  field  strength  is  nearly  constant; 
hence  the  torque  varies  directly  as  the  current  through 
the  armature.  In  a  series  motor,  on  the  other  hand, 
the  strength  of  field  varies  nearly  as  the  current,  and 
the  current  is  the  same  through  the  field  and  the  arma- 
ture. Hence  the  torque  varies  as  the  square  of  the  cur- 
rent. If  the  current  is  doubled,  it  is  doubled  in  both 
the  field  and  the  armature,  and  the  torque  is  therefore 
quadrupled.  The  series  motor  is  accordingly  used  where 
a  large  starting  torque  is  required,  as  in  cranes  and  motor 
vehicles. 


STARTING   RESISTANCE  429 

529.  Back  E.  M.  F.  in  a  Motor.  —  Connect  an  incandescent 
lamp  on  the  lighting  circuit  in  series  with  a  small  motor.  Clamp  the 
armature  or  hold  it  stationary,  and  turn  on  the  current.  The  lamp 
will  glow  with  full  brilliancy.  Next  let  the  motor  run  at  full  speed 
without  load ;  the  lamp  will  now  grow  dim. 

If  the  motor  is  provided  with  a  flywheel  to  keep  up  its  motion 
when  the  current  is  shut  off,  the  lamp  and  the  motor  may  be  con- 
nected to  the  mains  in  parallel.  Then  when  the  motor  is  running  at 
full  speed,  the  lamp  will  glow  with  nearly  or  quite  normal  brilliancy. 
Now  open  the  switch,  cutting  off  both  the  lamp  and  the  motor  from 
the  mains ;  the  lamp  will  glow  for  a  few  seconds  nearly  as  brightly 
as  before  the  main  circuit  was  opened. 

The  first  experiment  shows  that  the  motor  running 
takes  less  current  than  when  the  armature  is  held  fast. 
But  since  the  resistance  in  circuit  remains  unchanged, 
the  lessened  current  by  Ohm's  law  must  be  ascribed  to  a 
smaller  E.M.F.  The  fact  is,  the  motor  produces  a  back 
E.M.F.  nearly  equal  to  the  applied  E.M.F.  Denote  the 
back  E.M.F.  by  E1 ;  then  by  Ohm's  law 

T_E-E' 
R 

Since  the  -current  is  small  when  the  motor  is  running. 
E'  must  be  nearly  equal  to  E. 

The  second  experiment  shows  the  back  E.M.F.  directly, 
for  it  lights  the  lamp  so  long  as  the  motor  is  kept  running 
by  the  energy  stored  in  the  flywheel  after  shutting  off 
both  the  lamp  and  the  motor  from  the  supply  mains.  The 
armature  revolves  in  a  magnetic  field  and  generates  an 
E.M.F.  for  the  same  reason  that  it  does  when  spun  as  a 
generator. 

530.  Starting  Resistance.  —  The  resistance  of  a  motor 
armature  is  small,  and  a  motor  at  rest  has  no  back 
E.M.F.  to  limit  the  current.  If  therefore  the  current 
were  turned  on  without  temporary  starting  resistance  in 


430 


DYNAMO-ELECTRIC  MACHINERY 


circuit,  there  would  be  a  great  rush  of  current,  which 
might  damage  the  motor,  blow  the  line  fuses,  and  possibly 
throw  open  the  automatic  circuit  breaker  in  the  power 
house.  Hence  the  use  of  a  starter,  which  is  a  rheostat 

with  a  number  of  graduated 
resistances  (Fig.  454). 
When  the  switch  arm  is 
turned  to  touch  the  first  live 
contact  point,  the  circuit  is 
closed  through  enough  re- 
sistance to  avoid  danger. 
As  the  motor  speeds  up  and 
generates  larger  and  larger 
back  E.M.F.,  the  resist- 
ance is  gradually  cut  out 
by  moving  the  switch  arm 
to  successive  contact  points, 
until  the  starting  resistance 
is  all  out  and  the  motor  is 

running  at  full  speed.  In  the  figure  A  is  the  armature 
and  JP.the  field  coil  of  a  shunt  motor. 

The  switch  arm  is  often  held  in  place  by  a  release 
magnet  M  after  the  entire  starting  resistance  is  cut  out. 
If  the  line  switch  is  opened,  or  the  circuit  broken  in  any 
other  way,  the  magnet  releases  the  arm  and  a  spring 
throws  it  back  to  open  circuit.  This  prevents  injury  if 
the  current  should  suddenly  come  on  again. 

531.  Electric  Railways.  — The  electric  current  is  usually 
conveyed  to  the  moving  car  by  trolley  wire,  a  third  rail,  or 
by  a  conductor  laid  in  a  slot-conduit  between  the  rails. 
Direct  current  under  an  electric  pressure  of  550  volts  is 
nearly  always  used.  A  feeder  wire  is  often  employed  to 
prevent  too  great  a  drop  in  voltage  at  distant  points 


FIGURE  454.  —  STARTING  RESISTANCE 
FOR  MOTOR. 


THE  ALTERNATOR  431 

(Fig.  455).  The  circuit  is  from  the  positive  brush  of 
the  generator  to  the  feeder  and  trolley  wires  or  third  rail, 
thence  through  the  motors  to  the  car  wheels  and  track, 
and  so  back  to  the  negative  terminal  of  the  generator. 

Each  car  is  equipped  with  two  series  wound,  four- 
pole  motors.  They  drive  the  wheels  through  a  single 
reduction  gear.  At  starting,  the  "  controller  "  or  start- 


re   | 


Rails 

FIGURE  455.  —  ELECTRIC  RAILWAY  AND  FEEDER. 

ing  rheostat  places  the  two  motors  in  series  with  some 
resistance.  After  the  car  has  started,  this  resistance  is 
first  cut  out;  then  the  motors  are  joined  in  parallel  with 
resistance  in  circuit;  this  resistance  is  finally  cut  out 
after  the  car  attains  sufficient  speed.  As  the  motor 
speeds  up  it  generates  a  back-electromotive  force,  which 
reduces  the  current  to  its  working  value. 

II.     ALTERNATORS  AND  TRANSFORMERS 

532.  The  Alternator.  —  If  the  ends  of  the  armature  coil 
are  connected  to  two  slip-rings  (Fig.  456)  by  which  slid- 
ing contact  is  made  with  the 
brushes  A  and  B  and  the  external 
circuit,  the  machine  becomes  an 
alternator,  and  the  current  flowing 
in  the  external  circuit  CD  will 

alternate  or   reverse,   as   it   does 

.,  ,.  FIGURE  456.  —  SLIP-RINGS. 

in  an  armature  coil,  every  time 

the  armature  turns  through  the  angular  distance  from  one 
pole  to  the  next* 


432 


DYNAMO-ELECTRIC  MACHINERY 


A  complete  series  of  changes  in  the  current  and  E.M.F. 
in  both  directions  takes  place  while  the  armature  is  turn- 
ing from  one  pole  to  the  next  one  of  the  same  name. 
Such  a  series  of  changes  is  called  a  cycle.  The  frequency, 
or  the  number  of  cycles  per  second,  is  equal  to  the  product 
of  the  number  of  pairs  of  poles  on  the  field  magnet  and 

the  number  of  rotations 
per  second.  Frequencies 
are  now  restricted  be- 
tween the  limits  of  about 
25  and  60  cycles  per 
second.  Multipolar  ma- 
chines are  used  to  avoid 
excessive  speed  of  rota- 
tion. 

Figure  457  is  a  dia- 
grammatic sketch  of  an 
alternator  with  a  station- 
ary field  outside  and  an 
armature  rotating  with  the  shaft.  The  field  is  excited 
by  a  small  direct  current  machine  called  the  exciter.  The 
armature  coils  are  reversed  in  winding  from  one  field  pole 
N  to  the  next  S,  they  are  joined  in  series,  and  the  termi- 
nals are  brought  out  to  rings  B  on  the  shaft.  The 
brushes  bearing  on  these  rings  lead  to  the  external  circuit. 
533.  Alternators  with  Rotating  Field.  —  Since  the  rotation 
of  the  armature  with  respect  to  the  field  is  only  relative, 
it  clearly  makes  no  difference  in  the  generation  of  E.M.F. 
whether  the  armature  or  the  field  is  made  the  rotating 
member.  In  large  alternators  (A.  C.  generators)  the 
armature  is  the  stationary  member  outside  and  the  field 
rotates  within.  Slow  speed  generators  necessarily  have  a 
large  number  of  poles.  This  construction  follows  the 


FIGURE  457.  —  ALTERNATOR  WITH  STA- 
TIONARY FIELD. 


LAG   OF  CURRENT  BEHIND  E.  M.  F.  433 

best  engineering  practice,  since  it  permits  better  insula- 
tion of  the  armature  windings  on  the  stationary  member 
of  the  machine  and  avoids  the  transmission  of  high  volt- 
ages by  sliding  contacts  on  slip  rings. 

The  armature  core  is  built  up  from  punchings  of 
selected  steel  of  superior  magnetic  quality ;  these  punch- 
ings are  coated  with  insulating  varnish  to  reduce  eddy 
current  losses.  The  armature  punchings  are  securely 
bolted  together  between  two  cast-iron  rings  having  an 
I-beam  section.  Air  ducts  are  left  in  the  core  for  the 
purpose  of  ventilation. 

534.  Lag  of  Current  Behind  E.M.F.  —  When  the  circuit 
has  self -inductance,  an  alternating  E.M.F.  produces  a 
current  which  lags  behind  the  E..M.F. ;  and  as  a  conse- 
quence Ohm's  law  is  no  longer  adequate  to  express  its 
value.  The  self-inductance  not  only  introduces  an  addi- 
tional E.M.F.,  but  it  causes  the  current  to  come  to  its 
maximum  value  later  than 
the  E.M.F.  impressed  on 
the  circuit  by  the  generator. 

Figure  458  is  reproduced 
from  a  photograph  made  by 
the  E.M.F.  and  currents 
themselves  in  an  instru- 
ment called  an  oscillograph.  FlGURE  458. -LAG  OF  CURRENT  BE- 
T,  .  .  .  ,  £  ,  ,?  HIND  E.M.F. 

It  is  a  kind  of  double  gaL 

vanometer  in  which  the  movable  systems  have  so  short  a 
period  that  they  can  follow  all  the  oscillations  of  the 
current  and  E.M.F.  A  beam  of  light  is  reflected  from 
a  tiny  mirror  in  the  instrument  and  acts  on  a  rapidly 
moving  photographic  plate.  E  in  the  figure  is  the  curve 
of  the  impressed  E.M.F.  and  /that  of  the  current.  The 
latter  in.  this  case  came  to  its  maximum  nearly  a  quarter 


x\  /x\ 


434 


DYNAMO-ELECTRIC  MACHINERY 


FIGURE  459.  —  TWO-PHASE  CURRENTS. 


of  a  period  later  than  the    former.     (Trace  the  curves 
from  left  to  right.) 

535.   Polyphase  Alternators.  —  Two  or  more  currents  of 
the  same  frequency,  but  differing  in  phase  (§  196),  may 

be  obtained  from 
one  generator. 
Two-phase  or  three- 
phase  currents  are 
specially  useful  for 
the  transmission  of 
power  and  for  driv- 
ing induction  mo- 
tors; at  the  same 
time  they  are  just 

as  useful  for  lighting  purposes  as  the  current   from   a 
single-phase  machine. 

In  a  two-phase  alternator  there  are  two  sets  of  wind- 
ings, the  one  set  being  displaced  from  the  other  by  half 
the  pole  pitch ;  the  two  electromotive  forces  induced  in 
them  in  consequence  differ  by  a  quarter  of  a  period 
(Fig.  459).  When 
one  of  these  electro- 
motive forces  passes 
through  zero  value, 
the  other  will  be  at 
its  maximum. 

In  a  three-phase 
alternator  there  are 
three  separate  sets  of 
windings,  displaced 
from  one  another  by  two-thirds  of  the  pole  pitch.  There 
are  generated  thres  electromotive  forces  of  equal  ampli- 
tude, but  differing  in  phase  by  one-third  of  a  period 


c'  A'  B'  c' 

FIGURE  460.  —  THREE-PHASE  CURRENTS. 


TRANSFORMERS  435 

(Fig.  460).  The  three-phase  system  is  best  adapted  to 
the  transmission  of  power.  Three  lines  only  are  needed 
instead  of  six.  If  one  end  of  each  winding  is  brought 
to  a  common  junction,  and  the  other  ends  are  connected 
respectively  to  the  three  lines,  no  return  is  needed,  since 
each  line  in  succession  serves  as  the  return  for  the  other 
two.  This  may  be  understood  from  an  examination  of 
Figure  460,  which  shows  that  the  sum  of  the  two  currents 
or  electromotive  forces  in  one  direction  at  any  instant  is 
always  equal  to  the  third  in  the  other  direction;  in  other 
words,  the  algebraic  sum  of  the  three  is  always  zero. 

536.  Transformers.  —  A  transformer  is  an  induction  coil 
with  a  primary  of  many  turns  of  wire  and  a  secondary  of 
a  smaller  number,  both  wound  around  a  divided  iron  core 
forming  a  closed  magnetic  circuit ; 
that  is,  one  magnetic  circuit  is  in- 
terlinked with  two  electric  circuits 
(Fig.  461).  A  transformer  is  em- 
ployed with  alternating  currents 
either  to  step  down  from  a  high 
E.M.F.  to  a  low  one,  or  the  re- 
verse. The  two  electromotive  forces 
are  directly  proportional  to  the  num- 
ber of  turns  of  wire  in  the  two  coils. 

For  example,  to  reduce  a  2000-volt 
current  to  a  100-volt  current,  there 
must  be  20  turns  in  the  primary  to  every  one  in  the  sec- 
ondary. Both  coils  are  wound  on  the  same  iron  core,  and 
are  as  perfectly  insulated  from  each  other  as  possible. 
The  iron  serves  as  a  path  for  the  flux  of  magnetic  indue? 
tion,  and  all  the  lines  of  force  produced  by  either  coil 
pass  through  the  .other,  except  for  a  small  amount  of 
"magnetic  leakage."  When  the  secondary  is  open,  the 


436  DYNAMO-ELECTRIC  MACHINERY 

transformer  acts  simply  as  a  "  choke  coil " ;  that  is,  the 
self-induction  of  the  primary  is  so  large  that  only  sufficient 
current  is  transmitted  to  magnetize  the  iron  and  to  fur- 
nish the  small  amount  of  energy  lost  in  it. 

The  counter-E.M.F.  of  self-induction  is  then  nearly 
equal  to  the  E.M.F.  impressed  from  without.  But 
when  the  secondary  is  closed,  the  self-induction  is  sup- 
pressed to  the  extent  that  the  transformer  automati- 
cally adjusts  itself  to  the  condition  that  the  ,  energy 
in  the  secondary  circuit  lacks  only  a  few  per  cent  of  the 
energy  absorbed  by  the  primary  from  the  generator. 

537.  Transformers  in  a  Long-distance  Circuit.  —  The  utility 
of  the  transformer  lies  in  its  use  to  secure  high  voltage 
for  transmission  and  low  voltage  for  lighting  and  power. 
Only  small  currents  can  be  transmitted  over  distances 
exceeding  a  few  hundred  feet  without  excessive  heat  losses 


FIGURE  462.  —  TRANSFORMERS  ON  LONG-DISTANCE  CIRCUIT. 

on  account  of  the  resistance  of  the  conductors.  To  trans- 
mit power  while  still  keeping  the  current  small,  the  elec- 
tric pressure,  that  is,  the  number  of  volts,  must  be  increased, 
for  power  transmitted  in  watts  is  proportional  to  the  prod- 
uct of  the  number  of  volts  and  the  number  of  amperes. 
Figure  462  is  a  diagram  showing  a  transformer  system 
for  long-distance  power  transmission.  The  first  trans- 
former A  raises  the  potential  difference  from  2000  volts 
to  50,000  volts.  The  long  distance  transmission  takes 
place  at  this  voltage  to  the  second  transformer  B,  which 
steps  down  from  50,000  to  2000  volts  for  local  transmis- 


LONG  DISTANCE  TRANSMISSION  OF  POWER     437 

sion  within  the  limits  of  a  city  or  a  district.  The  third 
transformer  C  steps  down  further  from  2000  to  100  volts 
for  house  service  for  lighting,  fan  motors,  electric  cook- 
ing, electric  flatirons,  etc. 

538.  Long  Distance  Transmission  of  Power.  —  Power  is  now 
transmitted  over  long  distances  by  means  of  alternating 
currents  of  high  voltage.  The  transmission  is  invariably 


FIGURE  463. — CABLES  AND  TOWERS  OF  150,000- VOLT  LINE. 

by  three-phase  currents  over  one  or  two  sets  of  copper  or 
aluminum  cables,  strung  on  steel  towers  at  a  height  of 
about  75  feet.  These  cables  run  straight  from  point  to 
point  over  mountains,  valleys,  and  streams.  For  example, 
the  electric  power  generated  by  the  hydro-electric  plants 


438  DYNAMO-ELECTRIC  MACHINERY 

at  Niagara  Falls  is  raised  by  step-up  transformers  to 
60,000  volts  for  transmission  to  distant  cities,  —  Buffalo, 
Rochester,  Syracuse,  where  it  is  used  for  street  car  service, 
for  power  motors,  and  for  lighting  and  other  domestic 
purposes. 

At  Big  Creek  in  the  High  Sierras  in  California,  water 
power  to  the  extent  of  80,000  H.  P.  is  now  used  for  gen- 
erating three-phase  electric  currents  ;  the  voltage  is  raised 
by  step-up  transformers  to  150,000  for  transmission  over 
aluminum  cables  241  miles  to  the  Eagle  Rock  transformer 
station.  These  cables  are  0.96  inch  in  diameter,  and  are 
strung  17.5  feet  apart,  on  steel  towers  averaging  seven  to 
the  mile.  At  present  two  sets  of  three-wire  cables  are  in 
use,  each  set  strung  on  separate  towers  (Fig.  463).  Ulti- 
mately there  will  be  three  sets  for  the  transmission  of 
320,000  H.  P. 

At  Eagle  Rock  step-down  transformers  reduce  the  elec- 
tric pressure  to  15,000  volts  for  transmission  over  the 
Los  Angeles  district,  and  to  60,000  volts  for  the  Riverside 
district  and  beyond.  The  latter  district  adds  about  80 
miles  to  the  transmission,  making  320  miles  as  a  maximum. 

539.  The  Rotating  Magnetic  Field.  —  It  is  of  first  im- 
portance to  understand  how  a  magnetic  field  may  rotate 
while  the  coils  producing  the  field  stand  still;  for  the 
rotating  field,  invented  by  Ferraris  and  Tesla,  is  the  secret 
of  all  A.  C.  induction  motors  for  two-  or  three-phase 
currents.  A  simple  experiment  will  help  to  clear  up  the 
problem. 

Suspend  a  heavy  ball  by  a  string  at  least  ten  feet  long  and  set  it 
swinging  north  and  south  with  an  amplitude  of  a  foot  or  more.  At 
the  instant  when  the  ball  stops  at  either  extremity  of  its  path,  strike 
it  a  blow  with  a  mallet  east  and  west.  This  blow  will  cause  an  east 
and  west  simple  harmonic  motion,  differing  in  phase  from  the  north 


HUGE  TRANSFORMERS  AND  SWITCHES,  MOREL  SUBSTATION, 
CHICAGO,  MILWAUKEE  AND  ST.  PAUL  RAILWAY. 


THE  ROTATING  MAGNETIC  FIELD  439 

and  south  one  by  a  quarter  of  a  period.  Further,  if  the  blow  is  de- 
livered with  the  right  force,  the  two  simple  harmonic  motions,  com- 
bined in  the  pendulum,  will  give  rise  to  uniform  circular  motion  of 
the  ball. 

This  experiment  shows  that  uniform  circular  motion 
may  be  produced  by  combining  two  simple  harmonic 
motions  at  right  angles  to  each  other,  of  the  same  period 
and  amplitude,  and  differing  in  phase  by  a  quarter  of  a 
period. 

An  alternating  current  in  a  coil  without  iron  produces 
an  alternating  magnetic  field  along  the  axis  of  the  coil. 
If  the  current  follows  the  simple  harmonic  or  sine  law, 
the  magnetic  field  will  follow  it 
also. 

Let  two  like  coils  be  set  with 
their    axes   at  right  angles  (Fig. 
464),  and  let  two-phase  currents  be    B: 
passed  through  them,  one  through 
coil  A  A  and  the  other  through  BB. 
Now    these    two    magnetic   fields 
produced   by  the    two-phase  cur- 
rents  are  similar  to  the  two  motions      FIGURE  464.  —  COILS  FOR 
of  the  ball  in  the   pendulum  ex- 
periment ;  and  they  combine  to  produce  a  rotating  mag- 
netic field  near  their  common  center.     A  small  magnetic 
needle  mounted  there  will  spin  around  rapidly.     This  is 
analogous  to  the  way  in  which  uniform  rotary  motion 
without  dead  points  may  be  produced  from  two  oscillatory 
motions  by  using  two  cranks  at  right  angles,  as  in  quarter- 
crank  engines,  the  one  impulse  following  the  other  at  one 
fourth  of  a  period. 

The  above  combination  of  two  coils  at  right  angles  is 
suitable  for  two-phase  currents  only.  Another  way  to 


440 


DYNAMO-ELECTRIC  MACHINERY 


A' 


FIGURE  465. — WIND- 
ING FOR  TWO-PHASE_RO- 
TATING  FIELD. 


make  a  rotating  magnetic  field  is  by  three-phase  currents. 
These  differ  in  phase  by  one  third  of  a  period  (or  120°). 
They  are  analogous  to  a  three-crank  engine  with  the  cranks 
set  at  angular  distances  of  120°. 

540.  Ways  of  Combining  the  Circuits.  —  The  coils  or  cir- 
cuits that  receive  the  polyphase  currents  may  be  combined 

in  several  ways.  In  Figure  465  for  a 
two-phase  system,  the  entire  ring  is 
wound  as  a  closed  circuit  like  a  Gramme 
ring,  and  the  four  line  wires  are  at- 
tached at  four  equidistant  points.  In- 
stead of  this  plan,  the  winding  may  be 
divided  into  four  separate  coils,  all 
having  corresponding  ends  connected 
to  a  common  junction,  the  other  four 
ends  being  joined  to  the  four  line 

wires,  AA'  for  one  circuit  and  BB'  for  the  other. 
For  a  three-phase  system  Figure  466  shows  the  mesh  or  A 

method  of  connection.     Again  the  three  coils  may  have  a 

corresponding  end  of  each  connected  to 

a  common  junction,  the  other  ends  re- 
maining for  the  three  line  wires.     This 

is  known  as  the  star  or  ^-connection. 
Again,  the  coils  may  not  be  wound 

upon  a  ring,  but  on  poles  projecting  in- 

wardo     In   large    multipolar    machines 

the  three-phase  coils  may  be  wound  on 

six,  nine,  or  a  larger  number  of  poles, 

multiples  of  three,  or  they  may  be  embedded  in  slots  as  in 

the  armature  or  stator  of  A.  C.  generators. 

541.  Induction  Motors.  —  In    1888    Ferraris    of    Italy 
mounted  within  coils  like  those  of  Figure  464  a  hollow  cop- 
per cylinder  on  pivots  at  top  and  bottom.     When  two-phase 


FIGURE  466. — 
WINDING  FOR  THREE- 
PHASE  ROTATING 
FIELD. 


ABOVE  :    STATOR  OF  A.  C.  GENERATOR  CONNECTED  TO  STEAM  TURBINE. 
BELOW:    FIELD  OF  THE  SAME. 


ABOVE:    STATOR  OF  THREE-PHASE  MOTOR. 
BELOW:    THREE-PHASE  MOTOR  COMPLETE. 


INDUCTION  MOTORS  441 

currents  are  passed  through  the  two  circuits  of  the  Ferra- 
ris apparatus,  the  copper  cylinder  is  set  rotating  in  the 
direction  of  the  rotating  field.  The  rotation  of  the  field 
causes  the  lines  of  force  to  cut  the  cylinder  and  currents 
are  induced  in  the  copper.  By  Lenz's  law  (§  499)  the 
cylinder  moves  in  the  direction  to  check  the  induction  in 
it;  it  is  therefore  dragged  in  the  same  direction  as  the 
rotation  of  the  magnetic  field.  The  cylinder  tends  to  ro- 


FIGURE  467.  — INDUCTION  MOTOR  WITH  "SQUIRREL  CAGE"  ROTOR. 

tate  as  fast  as  the  field,  but  never  quite  reaches  it;  for 
then  there  would  be  no  cutting  of  lines  of  force  and  no 
induction.  The  difference  in  speed  between  the  field  and 
the  rotor,  as  the  cylinder  is  called,  is  known  as  the  slip. 
If  a  little  friction  is  applied  to  the  cylinder,  the  slip  will 
increase  until  the  larger  induced  currents  are  just  sufficient 
to  supply  the  needed  torque. 

In  commercial  motors  the  actual  rotor  consists  of  a  cylin- 
drical core  built  up  of  thin  steel  disks,  with  slots  or  holes 
through  parallel  to  the  shaft.  In  these  are  embedded 
heavy  copper  rods  or  bars,  which  are  joined  together  at 


442 


D  TNAMO-EL ECTRIC  MA  CHINEE  Y 


their  ends,  so  as  to  form  a  "squirrel  cage"  of  copper  (Fig. 
467).  The  induced  currents  flow  in  the  rods.  The  rotor 
does  not  need  to  have  either  commutator  or  slip  rings 
and  is  entirely  separate  from  any  other  circuit.  Its  cur- 
rents are  wholly  inductive.  In  some  larger  forms  the 
rotor  is  wound  like  a  drum  armature,  and  the  coils  are 
connected  through  slip-rings,  so  that  resistance  may  be 
inserted  in  the  circuits  at  starting.  This  resistance  is  cut 
out  as  the  motor  gets  up  its  speed. 

III.   ELECTRIC  LIGHTING 

542.  The  Carbon  Arc.  —  In  1800  Sir  Humphry  Davy 
discovered  that  when  two  pieces  of  charcoal,  suitably  con- 
nected to  a  powerful  voltaic  battery,  were  brought  into 
contact  at  their  ends  and  were  then  separated  a  slight  dis- 
tance, brilliant  sparks  passed  between  them.  No  mention 

was  made  of  the  electric  arc  until 
1808.  With  a  battery  of  2000 
cells  and  the  carbons  in  a  hori- 
zontal line,  they  could  be  sepa- 
rated several  inches,  while  the 
current  was  conducted  across 
in  the  form  of  a  curved  flame  or 
arc.  Hence  the  name  electric 
arc  given  to  this  form  of  electric 
lighting. 

Dense  compressed  or  molded 
carbon  rods  are  now  used,  and 
when  they  are  separated  a  slight 
distance  they  are  heated  to  an  exceedingly  high  tempera- 
ture, and  the  current  from  a  dynamo  continues  to  pass 
across  through  the  heated  carbon  vapor,  which  is  ionized 
by  the  emission  of  eLQQteQnjs  from  the  negative  carbon. 


FIGURE  468.  —  THE  ARC  LIGHT, 
DIRECT  CURRENT. 


THE  OPEN  AND   THE  INCLOSED  ABC 


443 


The  ends  of  the  carbon  rods  in  the  open  air  are  disinte- 
grated, a  depression  or  "  crater "  forming  in  the  positive 
and  a  cone  on  the  negative  (Fig.  468).  Most  of  the  light 
of  the  open  arc  comes  from  the  bottom  of  this  crater,  the 
temperature  of  which  Violle  has  estimated  to  be  3500°  C. 
The  arc  light  may  be  produced  in  a  vacuum.  The  in- 
tense heat  is  not,  therefore,  generated  by  combustion.  It 
is  the  energy  of  the  current  converted  into 
heat  by  the  resistance  of  the  arc.  The  usual 
current  for  arc  lamps  is  from  5  to  10  amperes. 
For  searchlights,  arc  lights  of  great  power 
are  produced  by  the  use  of  thicker  carbons 
and  100  or  more  amperes. 

543.  The  Open  and  the  Inclosed.  Arc.  — To 
keep  the  carbon  rods  from  burning  away  too 
rapidly,  modern  arc  lamps  are  mostly  of  the 
"  inclosed  arc  "  type.  The  lower  carbon  and 
a  part  of  the  upper  one  are  inclosed  in  a 
small  glass  globe,  which  is  air-tight  at  the 
bottom,  but  allows  the  upper  carbon  to  slip 
through  a  check-valve  at  the  top  (Fig.  469). 
Soon  after  the  arc  begins  to  burn,  the  oxygen  in  the  globe 
is  absorbed  and  the  arc  is  then  inclosed  in  an  atmosphere 
of  nitrogen  from  the  air  and  of  carbon  monoxide  from 
the  incomplete  combustion  of  the  carbon.  The  inclosed 
arc  is  longer  than  the  open  arc,  and  the  E.M.F.  is  about 
80  volts  instead  of  50  as  required  by  the  open  arc;  but 
the  current  for  the  inclosed  arc  is  smaller  than  for  the 
open  arc.  The  carbons  for  the  inclosed  arc  last  at  least 
ten  times  as  long  as  in  the  open  air. 

The  direct  current  inclosed  arc  is  operated  at  a  higher 
temperature  than  the  alternating  current  lamp,  and  is 
therefore  more  efficient. 


FIGURE  469. 
—  THE  IN- 
CLOSED ARC. 


444  DYNAMO-ELECTRIC  MACHINERY 

544.  Other  Arc  Lights.  —  Other  arc  lamps  are  now  in 
commercial  use  in  which  the  light  comes  chiefly  from  the 
incandescent  stream  between  the  electrodes.  They  have 
a  higher  efficiency  than  the  carbon  arc.  In  the  metallic 
arc  powdered  magnetite  in  an  iron  tube  is  used  for  one 
electrode  and  a  block  kof  copper  for  the  other.  The  arc 
flame  is  very  white  and  brilliant,  the  light  coming  from 
the  luminous  iron  vapor. 

Flaming  arcs  are  made  by  the  use  of  a  positive  electrode 
impregnated  with  salts  of  calcium,  chiefly  calcium  fluoride. 
The  light  from  the  flaming  arc  is  yellow,  and  is  adapted 
to  outdoor  illumination  only. 

The  mercury  arc  of  Cooper  Hewitt  is  radically  different 
from  other  arc  lamps.  It  has  the  arc  in  a  sealed  tube, 
which  is  exhausted  of  air,  and  the  light  comes  from  lumi- 
nous mercury  vapor.  It  consists  of  a  glass  tube  one  inch 
in  diameter  and  from  20  to  50  inches  long,  with  a  bulb  at 
one  end  for  holding  mercury,  and  a  small  iron  electrode  at 
the  other.  A  special  device  must  be  used  to  start  the 
current.  This  light  contains  no  red 
rays  and  thus  gives  a  peculiar  color  to 
objects  illuminated  by  it.  This  lamp 
operates  by  direct  current  only. 

545.  Carbon  Filament  Lamps.  —  The 
principle  of  the  incandescent  lamp  is 
the  use  of  a  filament  or  wire  of  such 
high  resistance  that  it  can  be  brought 

FIGURE  470.  —  CAR-  ^o  glow  by  the  passage  of  an  electric 
BON  FILAMENT  LAMP.  '  *  7  .  .  ,  ,  . 

current.     The  filament  is  inclosed  in  a 

glass  bulb,  exhausted  of  air,  and  has  its  ends  connected 
through  the  glass  by  short  pieces  of  platinum  wire  (Fig. 
470).  The  carbon  filament  is  now  made  from  cellulose 
obtained  from  cotton. 


METAL  FILAMENT  LAMPS  445 

The  temperature  to  which  a  carbon  filament  can  be  raised 
is  limited  by  the  tendency  of  the  carbon  to  vaporize  at  high 
temperatures.  The  carbon  thrown  off  rapidly  reduces  the 
thickness  of  the  filament  and  blackens  the  globe.  The 
useful  life  of  a  carbon  filament  is  from  500  to  700  hours. 

The  ordinary  commercial  unit  for  the  carbon  filament  is 
the  16-candle  power  lamp.  On  a  110-volt  circuit  it  takes 
about  0.5  ampere.  Since  the  power  in  watts  consumed  is 
El,  this  lamp  requires  about  55  watts,  or  3.5  watts  per 
candle.  The  efficiency  of  a  lamp  is  expressed  in  watts  per 
candle.  The  efficiency  of  the  carbon  filament  lamp  is  from 
3.1  to  3.5  watts  per  candle. 

A  metallized  filament  is  obtained  by  heating  a  treated 
cellulose  filament  in  an  electric  'furnace  to  a  very  high 
temperature.  It  can  be  glowed  at  a  higher 
temperature  than  the  ordinary  carbon  fila- 
ment ;  it  has  a  corresponding  higher  ef- 
ficiency of  about  2.5  watts  per  candle  for 
50  and  60  watt  lamps. 

546.  Metal  Filament  Lamps.  —  Metal  wires 
cannot  be  used  in  glow  lamps  unless  their 
melting  point  is  higher  than  that  of  plati- 
num. The  melting  point  of  platinum  is  FIGURE  471.- 
about  1775°  and  that  of  tungsten  about  TUNGSTEN  FILA- 
3200°  C.  The  available  metals  for  incan-  MENT  LAMP' 
descent  lamps  are  tantalum  and  tungsten.  Their  specific 
resistance  is  lower  than  that  of  carbon  ;  hence  filaments 
made  of  them  must  be  longer  and  thinner  than  those  of 
carbon.  A  piece  of  tungsten  as  large  as  a  lead  pencil 
contains  enough  material  to  make  about  five  miles  of  wire 
for  40  watt  lamps.  A  continuous  tungsten  filament  is  so 
long  that  it  must  be  wound  zigzag  on  a  light  frame  or  reel 
.(Fig.  471).  The  tungsten  25  watt  lamp  gives  20  candle 


446 


DYNAMO-ELECTRIC  MACHINERY 


power,  or  1.25  watts  per  candle.  By  reason  of  its  high 
efficiency  it  has  largely  displaced  the  carbon  lamp,  in  spite 
of  the  fact  that  it  is  more  fragile.  The  tungsten  lamp 
has  a  useful  life  of  from  800  to  1000  hours. 

547.  Gas-filled    Lamps.  —  In    many    early   lamp   experi- 
ments the  glass  bulbs,  after  exhaustion  of  air,  were  filled 
with  an  inert  gas.     This  practice  was  soon  abandoned  be- 
cause the  efficiency  was  lowered  by  the  heat 
carried  away  from  the  filament  to  the  bulb 
by  convection  in  the  gas.     In  recent  develop- 
ments it  has  been  found  that  gas  can  be  used 
to  advantage  with  filaments  of  large  cross- 
section  in  high  power  lamps.     When  the  bulb 
of  a  lamp  taking  more  than  75  watts  is  filled 
with  an  inert  gas,  like  nitrogen  or  a,rgon,  it 
is  possible  to  raise  the  temperature  of   the 

filament  and  in  this  way  to  get  a  higher  efficiency.  In 
thicker  filaments  the  loss  of  heat  by  convection  is  more 
than  offset  by  the  gain  secured  by  the  use  of  a  higher 
temperature.  The  twenty  ampere  series  lamp,  filled  with 
argon,  has  an  efficiency  of  half  a  watt  per  candle.  In 
other  words,  a  500  watt  lamp  has  a  candle  power  of  1000. 
These  lamps  are  specially  adapted  to  the  lighting  of  large 
areas  and  city  streets  (Fig.  472). 

548.  Incandescent   Lamp  Circuits. — Incandescent   lamps 
are  connected  in  parallel  between  the  mains  in  a  building. 


FIGURE  472. 
—  GAS-FILLED 
LAMP. 


FIGURE  473.  —  INCANDESCENT 
LAMP  CIRCUIT, 


FIGURE  474.  —  LAMP  CIRCUIT  WITH 
TRANSFORMER, 


THE  TRANSMITTER   OR  KEY  447 

These  mains  lead  either  directly  to  a  dynamo  (Fig.  473), 
or  to  the  low  voltage  side  of  a  transformer  in  the  case  of 
alternating  currents  (Fig.  474).  Single  lamps  are  turned 
off  usually  by  the  key  in  the  socket  (Fig.  470),  and  groups 
of  lamps  by  a  switch  S  (Fig.  474). 

IV.     THE  ELECTRIC  TELEGRAPH 

549.  The  Electric  Telegraph  is  a  system  of  transmitting 
messages  by  means  of  simple  signals  through  the  agency 
of  an  electric  current.     Its  essential  parts  are  the  line, 
the  transmitter  or  key,  the  receiver  or  sounder,  and  the 
battery. 

550.  The  Line  is  an  iron,  copper  or  phosphor-bronze  wire, 
insulated  from  the  earth  except  at  its  ends,  and  serving  to 
connect  the  signaling  apparatus.     The  ends  of  this  con- 
ductor are  connected  with  large  metallic  plates,  or  with 
gas  or  water  pipes,  buried  in  the  earth.     By  this  means 
the  earth  becomes  a  part  of  the  electric  circuit  containing 
the  signaling  apparatus. 

551.  The  Transmitter  or  Key  (Fig.  475)  is  merely  a  cur- 
rent interrupter,  and  usually  consists  of  a  brass  lever  A, 
turning  about  pivots  at  B.     It 

is  connected  with  the  line  by 

the  screws    0  and   D.     When 

the   lever  is   pressed   down,    a 

platinum  point  projecting  under 

the  lever  is  brought  in  contact     F^^S.-^TELEGRAPH  KEY. 

with    another    platinum    point 

E,   thus    closing    the    circuit.       When   not    in    use,  the 

circuit  is  left  closed,  the  switch  F  being  used  for  that 

purpose. 

552.  The  Receiver  or  Sounder  (Fig.  476)  consists  of  an 
electromagnet  A  with  a  pivoted  armature  B.     When  the 


448 


DYNAMO-ELECTRIC  MACHINERY 


FIGURE  476. — TELEGRAPH  SOUNDER. 


circuit  is  closed  through  the  terminals  D  and  E,  the  arma 
ture  is  attracted  to  the  magnet,  producing  a  sharp  click. 

When  the  circuit  is 
broken,  a  spring  C 
causes  the  lever  to  rise 
and  strike  the  backstop 
with  a  lighter  click. 

553.  The  Belay.  — 
When  the  resistance  of 
the  line  is  large,  the 
current  is  not  likely  to 
be  strong  enough  to  operate  the  sounder  with  sufficient 
energy  to  render  the  signals  distinctly  audible.  To 
remedy  this  defect,  an  electromagnet,  called  a  relay  (Fig. 
477),  whose  helix  A  is  composed  of  many  turns  of  fine 
wire,  is  placed 
in  the  circuit  by 
means  of  its  ter- 
minals O  and  D. 
As  its  armature 
moves  to  and  fro 
between  points, 
it  opens  and 
closes  a  shorter  local  circuit  through  E  and  _F,  in  which 
the  sounder  is  placed.  Thus  the  weak  current,  through 
the  agency  of  the  relay,  brings  into  action  a  current 
strong  enough  to  work  the  local  sounder  with  a  loud 
click. 

554.  The  Battery  consists  of  a  large  number  of  cells, 
usually  of  the  gravity  type,  connected  in  series.  It  is 
generally  divided  into  two  sections,  one  placed  at  each 
terminal  station,  these  sections  being  connected  in  series 
through  the  line.  The  principal  circuits  of  the  great 


FIGURE  477.  —  TELEGRAPH  RELAY. 


Alexander   Graham   Bell 

was  born  in  Edinburgh,  Scot- 
land, in  1847.  His  father, 
Alexander  Melville  Bell,  was 
a  teacher  and  inventor.  The 
son  came  to  the  United  States 
in  1 872  and  became  professor 
at  Boston  University.  While 
there  he  invented  the  tele- 
phone in  1875.  He  also  in- 
vented the  photophone,  and 
developed  his  father's  system 
of  phonetics. 


Samuel    F.     B.     Morse 

(1791-1872)  was  born  at 
Charlestown,  Massachusetts, 
and  died  in  New  York  City. 
After  graduating  from  Yale 
at  the  age. of  nineteen,  he 
studied  art  in  England  under 
Benjamin  West.  In  1832  he 
perfected  the  electric  tele- 
graph, and  in  1843  was 
granted  an  appropriation  by 
Congress  for  a  line  between 
Washington  and  Baltimore. 
In  1844  this  line  was  com- 
pleted,—  the  first  successful 
electric  telegraph  on  a  large 
scale. 


THE  ELECTRIC  BELL 


449 


Sounder 


i|i|Hh. 

Line  Battery 


telegraph  companies  are  now  worked  by  means  of  currents 

from  dynamo  machines. 

555.  The  Signals  are  a  series  of  sharp  and  light  clicks 

separated  by  intervals  of  silence  of  greater  or  less  dura- 
tion, a  short  interval  between  the 
clicks  being  known  as  a  "  dot,"  and 
a  long  one  as  a  "  dash."  By  a  com- 
bination of  "  dots  "  and  "  dashes," 
letters  are  represented  and  words  are 
spelled  out. 

556.  The  Telegraph  System  described 
in  the  preceding  sections  is  known 
as  Morse's,  from  its  inventor.  Fig- 
ure 478  illustrates  diagrammatically 
the  instruments  necessary  for  one 
terminal  station,  together  with  the 
mode  of  connec- 
tion. The  ar- 
rangement at  the 
other  end  of  the 

line  is  an  exact  duplicate  of  this  one, 

the  two  sections  of  the  battery  being 

placed  in  the  line,  so  that  the  negative 

pole  of  one  and  the  positive  pole  of  the 

other  are   connected  with  the  earth. 

At  intermediate  stations  the  relay  and 

the  local  circuit  are  connected  with  the 

line  in  the  same  manner  as  at  a  termi- 
nal station. 

557.   The  Electric  Bell  (Fig.   479)  is 

used  for  sending  signals  as  distinguished  from  messages. 

Besides  the  gong,  it  contains  an  electromagnet,  having 

one  terminal  connected  directly  with  a  binding-post,  and 


irth 


r^Ear 

FIGURE  478.  —  TERMI- 
NAL INSTRUMENTS  ON 
TELEGRAPH  LINE. 


FIGURE  479.  —  ELEC- 
TRIC BELL. 


450 


DYNAMO-ELECTRIC  MACHINERY 


FIGURE  480.  —  PUSH- 
BUTTON. 


the  other  through  a  light  spring  attached  to  the  armature 
(shown  on  the  left  of  the  figure)  and  a  contact  screw, 
with  another  binding-post.  One  end  of  the  armature  is 
supported  by  a  stout  spring,  or  on  pivots, 
and  the  other  carries  the  bent  arm  and 
hammer  to  strike  the  bell.  Included 
in  the  circuit  are  a  battery  and  a  push- 
button B,  shown  with  the  top  unscrewed 
in  Fig.  480. 

When  the  spring  E  is  brought  into 
contact  with  D  by  pushing  (7,  the  cir- 
cuit is  closed,  the  electromagnet  attracts 
the  armature,  and  the  hammer  strikes 
the  gong.  The  movement  of  the  arma- 
ture opens  the  -circuit  by  breaking  contact  between  the 
spring  and  the  point  of  the  screw ;  the  armature  is  then 
released,  the  retractile  spring  at  the  bottom  carries  it 
back,  and  contact  is  again  estab- 
lished between  the  spring  and  the 
screw.  The  whole  operation  is  re- 
peated automatically  as  long  as  the 
circuit  is  kept  closed  at  the  push- 
button. A  "  buzzer  "  is  an  electric 
bell  without  the  hammer  and  gong. 
Instead  of  two  dry  cells  for  ring- 
ing house  bells,  a  small  step-down 
transformer  connected  to  the  light- 
ing wires,  with  the  bells  in  circuit 
on  the  low  voltage  side,  gives  satisfactory  service  (Fig. 
481).  The  bells  need  not  be  changed  in  any  way, 
since  the  frequency  of  the  current  is  too  high  to  per- 
mit them  to  respond  without  the  usual  automatic  circuit 
breaker. 


FIGURE  481.  —  TRANS- 
FORMER FOR  RINGING 
BELLS. 


THE  MICROPHONE 


451 


FIGURE  482.  —  THE  MODERN 
TELEPHONE. 


V.    THE  TELEPHONE 

558.  The  Telephone  (Fig.  482)  consists  of  a  horseshoe 
magnet  0,  both  poles  of  which  are  surrounded  by  a  coil  of 
many  turns  of  fine  copper 
wire  whose  ends  are  con- 
nected  with  the  binding- 
posts  t  and  t.  At  right 
angles  to  the  magnet,  and 
not  quite  touching  the 
poles,  within  the  coils,  is  an 
elastic  diaphragm  or  disk 
of  soft  sheet-iron,  kept 
in  place  by  the  conical 
mouthpiece  d.  If  the  in- 
strument is  placed  in  an 
electric  circuit  when  the  current  is  unsteady,  or  alternat- 
ing in  direction,  the  magnetic  field  due  to  the  helix,  when 
combined  with  that  due  to  the  magnet,  alters  intermit- 
tently the  number  of  lines  of  force  which  branch  out  from 
the  poles,  thus  varying  the  attraction  of  the  magnet  for 
the  disk.  The  result  is  that  the  disk  vibrates  in  exact 

keeping  with  the  changes  in  the 
current. 

559.  The  Microphone  is  a  device 
for  varying  an  electric  current 
by  means  of  a  variable  resistance 
in  the  circuit.  One  of  its  simplest 
forms  is  shown  in  Figure  483.  It 
consists  of  a  rod  of  gas-carbon 
A,  whose  tapering  ends  rest  loosely  in  conical  depressions 
made  in  blocks  of  the  same  material  attached  to  a  sound- 
ing board.  These  blocks  are  placed  in  circuit  with  a 


FIGURE  483.  —  MICROPHONE. 


452 


D  TNAMO-ELECTRIC  MA  CHINEE  T 


battery  and  a  telephone.  While  the  current  is  passing, 
the  least  motion  of  the  sounding  board,  caused  either  by 
sound  waves  or  by  any  other  means,  such  as  the  ticking 
of  a  watch,  moves  the  loose  carbon  pencil  and  varies  the 
pressure  between  its  ends  and  the  supporting  bars.  A 
slight  increase  of  pressure  between  two  conductors,  resting 
loosely  one  on  the  other,  lessens  the  resistance  of  the  con- 
tact, and  conversely.  Hence,  the  vibrations  of  the  sound- 
ing board  cause  variations  in  the  pressure  at  the  points 
of  contact  of  the  carbons,  and  consequently  make  cor- 
responding fluctuations  in  the  current  and  vibrations  of 
the  telephone  disk. 

560.  The  Solid  Back  Transmitter.  —  The  varying  resist- 
ance of  carbon  under  varying  pressure  makes  it  a  valuable 
material  for  use  in  telephone  trans- 
mitters. Instead  of  the  loose  con- 
tact of  the  microphone,  carbon  in 
granules  between  carbon  plates  is 
now  commonly  employed. 

The  form  of  transmitter  exten- 
sively used  for  long  distance  work 
is  the  "solid  back"  transmitter 
(Fig.  484).  The  figure  shows  only 
the  essential  parts  in  section,  minor 
details  being  omitted.  M  is  the 
mouthpiece,  and  F  and  C  the  front  and  back  parts  of  the 
metal  case.  The  aluminum  diaphragm  D  is  held  around 
its  edge  by  a  soft  rubber  ring.  The  metal  block  W  has  a 
recess  in  front  to  receive  the  carbon  electrodes  A  and  B. 
Between  them  are  the  carbon  granules.  The  block  E  is 
attached  to  the  diaphragm  and  is  insulated  from  W  ex- 
cept through  the  carbon  granules.  The  transmitter  is 
placed  in  circuit  by  the  wires  connected  to  W  and  18, 


FIGURE  484.  —  SOLID  BACK 
TRANSMITTER. 


FIELD  WIRELESS  OUTFIT  OF  THE  UNITED  STATES  ARMY. 
This  can  be  set  up  and  put  into  operation  in  seven  minutes. 


WIRELESS  ROOM  IN  A  TRANSATLANTIC  LINER. 


OSCILLATORY  DISCHARGES 


453 


Provision  is  made  for  an  elastic  motion  of  the  diaphragm 
and  the  block  E.  Sound  waves  striking  the  diaphragm 
cause  a  varying  pressure  between  the  plates  and  the  car- 
bon granules.  This  varying  pressure  varies  the  resist- 
ance offered  by  the  granules  and  so  varies  the  current. 
The  transmitter  is  in  circuit  in  the  line  with  the  primary 
of  a  small  induction  coil,  the  secondary  being  in  a  local 
circuit  with  the  telephone  receiver.  The  induced  currents 
in  the  secondary  have  all  the  peculiarities  of  the  primary 
current ;  and  when  they  pass  through  a  receiver,  it  re- 
sponds and  reproduces  sound  waves  similar  to  those  which 
disturb  the  disk  of  the  transmitter. 

VI.   WIRELESS  TELEGRAPHY 

561.  Oscillatory  Discharges.  — The  discharge  of  any  con- 
denser through  a  circuit  of  low  resistance  is  oscillatory. 
The  first  rush  of  the  discharge  surges  beyond  the  condi- 
tion of  equilibrium,  and  the 
condenser  is  charged  in  the 
opposite  sense.  A  reverse 
discharge  follows,  and  so 
on,  each  successive  pulse 
being  weaker  than  the  pre- 
ceding, until  after  a  few 
surges  the  oscillations  cease. 
Figure  485  was  made  from 
a  photograph  of  the  oscil- 
latory discharge  of  a  con- 
denser by  means  of  a  very  small  mirror,  which  reflected 
a  beam  of  light  on  a  falling  sensitized  plate.  Such  alter- 
nating surges  of  high  frequency  are  called  electric  oscil- 
lations. Joseph  Henry  discovered  long  ago  that  the 
.  discharge  of  a  Leyden  jar  is  oscillatory. 


FIGURE  485.  —  OSCILLATORY  DIS- 
CHARGE. 


454  DYNAMO-ELECTRIC  MACHINERY 

562.  Electric  Waves.  —  In  1887-1888  Hertz  made  the 
discovery  that  electric  oscillations  give  rise  to  electric 
waves  in  the  ether,  know  as  Hertzian  waves,  which  ap- 
pear to  be  the  same  as  waves  of  light,  except  that  they 
are  very  much  longer,  or  of  lower  frequency.  They  are 
capable  of  reflection,  refraction,  and  polarization  the  same 
as  light. 

Evidence  of  these  waves  may  be  readily  obtained  by 
setting  up  an  induction  coil,  with  two  sheets  of  tin-foil  on 
glass,  Q  and  (X,  connected  with  the  terminals  of  the  sec- 


FIGURE  486.  —  ELECTRIC  WAVE  TRANSMITTER. 

ondary  coil,  and  with  two  discharge  balls,  F  and  F',  as 
shown  in  Fig.  486.  So  simple  a  device  as  a  large  picture 
frame  with  a  conducting  gilt  border  may  be  used  to  detect 
waves  from  the  tin-foil  sheets.  If  the  frame  has  shrunken 
so  as  to  leave  narrow  gaps  in  the  miter  at  the  corners, 
minute  sparks  may  be  seen  in  a  dark  room  breaking  across 
these  gaps  when  the  induction  coil  produces  vivid  sparks 
between  the  polished  balls,  F  and  F1 .  The  plane  of  the 
frame  should  be  held  parallel  with  the  sheets  of  tin-foil. 
The  passage  of  electric  waves  through  a  conducting  circuit 
produces  electric  oscillations  in  it,  and  these  oscillations 
cause  electric  surges  across  a  minute  air  gap. 


CRYSTAL  DETECTORS  455 

563.  The  Coherer.  —  One  of  the  earliest  devices  for  the 
detection    of    electric  waves  is  the   coherer   (Fig.    487). 
When  metal  filings  are  placed  loosely  between  solid  elec- 
trodes in  a  glass  tube  they  offer  a  high  resistance  to  the 
passage  of  an  electric  current;  ~ 

but  when    electric    oscillations  J*^  j^Jf  ^ > 

— vT  :j— - — — V       t-^  j) — 

are  produced  in  the  neighbor- 

,        ,      „  ,,      ,    i       ,,  .   .  FIGURE  487.  —  THE  COHERER. 

hood  of  the  tube,  the  resistance 

of  the  filings  falls  to  so  small  a  value  that  a  single  voltaic 
cell  sends  through  them  a  current  strong  enough  to  work 
a  relay  (§  553).  If  the  tube  is  slightly  jarred,  the  filings 
resume  their  state  of  high  resistance.  A  minute  discharge 
from  the  cover  of  an  electrophorus  (§  432)  through  the 
filings  lowers  the  resistance  just  as  electric  oscillations 
do.  It  is  thought  that  minute  sparks  between  the  filings 
partially  weld  them  together  and  make  them  conducting. 

564.  Crystal  Detectors.  —  The  coherer  is   now  obsolete 
and  more  sensitive  detectors  have  been  discovered.     The 
object  aimed  at  in  most  of  them  is  the  rectification  of  the 
rapid  oscillations  from  the  receiving  antenna  or  aerial  wire, 
so  as  to  secure  a  unidirectional  discharge  which  will  affect 
a  telephone.     On  account  of  its  high  self-inductance,  a 
telephone  acts  as  a  choke  coil  to  high  frequency  electric 
oscillations  and  will  not  respond  to  them.     It  has  been 
found  that  certain  crystals,  such  as  polished  silicon,  galena, 
and  carborundum,  possess  a  unilateral  conductivity  for 
electricity.     A  crystal  of  carborundum  may  have  three  or 
four  thousand  times  as  great  conductivity  in  one  direction 
as  in  the  opposite  for  certain  voltages.     Hence,  if  a  crystal 
detector  is  inserted  in  the  oscillation  circuit  of  a  receiver, 
it  rectifies  the  oscillations  in  a  train  of  electric  impulses, 
to  which  a  telephone  will  respond  with  a  sound  correspond- 
ing in  pitch  to  the  number  of  impulses  per  second. 


456 


DYNAMO-ELECTRIC  MACHINERY 


The  crystal  is  held  in  a  conducting  holder  and  is  touched 
lightly  by  a  metal  point  (Fig.  488).  The  brass  cup  shown 
in  the  figure  holds  the  crystal  securely  by  means  of 

three  set  screws.  Another 
method  of  mounting  is  to 
embed  the  crystal  in  a  soft 
alloy  which  melts  at  a  low 
temperature.  The  contact 
wire  can  be  moved  about  so 

FIGURE  488.  -  HOLDER  FOR  CRYS-     aS  tO  find  the  Sensitive  spots 
TAL  DETECTOR.  in  the  crystal. 

565.  The  Audion  is  a  very  sensitive  detector,  depending  for  its 
action  on  the  fact  that  electrons  are  thrown  off  from  the  negative  end 
of  an  incandescent  filament  in  an  exhausted  (or  partly  exhausted) 
bulb.  If  the  bulb  has  supported  in  it  a  plate  surrounding  the  fila- 
ment (Fig.  489),  a  single  voltaic  cell  will  send  a  (negative)  current 
from  its  negative  electrode  to  the  negative  end  of  the  hot  filament, 
thence  through  the  space  in  the  bulb  to  the  metal  plate,  and  out 
to  the  other  pole  of  the  voltaic 
cell.  No  current  will  flow  unless 
the  negative  pole  of  the  cell  is 
connected  to  the  negative  of  the 
filament.  This  arrangement  is 
therefore  an  electric  valve  or  rec- 
tifier, which  lets  electric  impulses 
through  in  one  direction  and  not 
in  the  other.  Fleming  calls  it 
an  "oscillation  valve."  In  the 
figure,  oscillations  in  one  direc- 
tion from  the  oscillation  trans- 
former T  will  pass  through  the 
circuit,  including  the  valve  V  and 
the  telephone  P,  but  not  those  FlGURE  489  ~ '•  OSCILLATION 

,.     '  VALVE." 

in  the  other  direction. 

The  auction  is  a  modification  of  the  "  oscillation  valve  "  of  Fleming, 
which  becomes  a  relay  for  the  aerial  oscillations  to  operate  receiving 


TRANSMITTING  AND   RECEIVING   CIRCUITS       457 


HI 


telephones  in  a  circuit  with  a  battery  (Fig.  490).  In  addition  to  the 
hot  filament  and  the  metal  plate  the  audion  has  a  "  grid  "  consisting 
of  a  coil  of  copper  wire,  which  is  one  terminal* of  the  circuit  from 
the  receiving  helix.  The 
other  terminal  of  this  cir- 
cuit is  joined  to  the  fila- 
ment. The  negative  of  the 
adjustable  battery  .B  is 
joined  to  the  negative  end 
of  the  filament.  The  recti- 
fied train  of  impulses  passes 
through  from  the  hot  fila- 
ment to  the  copper  coil. 
The  passage  of  these  impulses 
causes  similar  impulses  from 
the  battery  B  to  pass  between 
the  Jilament  and  the  metal 
plate,  and  hence  through  the 
receiving  telephone  T.  FIGURE  490.  —  THE  AUDION. 

566.  Transmitting  and  Receiving  Circuits.  —  A  simple 
tuned  transmitting  circuit  for  wireless  telegraphy  is  illus- 
trated in  Figure  491,  where  I 
is  an  induction  coil,  O  a  con- 
denser, S  a  spark  gap,  H  a 
variable  helix,  A  the  aerial  or 
antenna,  and  E  the  earth  con- 
nection. 

Figure  492  is  a  correspond- 
ing simple  receiving  circuit. 
The  receiving  telephones  are 
shown  at  T,  the  detector  at  D, 
and  a  variable  condenser  at 
0.     These  arrangements   are 
capable  of  many  variations. 
The  magnetic  effect  of  a  rectified  train  of  electric  im- 
pulses is  never  reversed.     Hence  they  pass  through  the 


FIGURE  491.  —  TRANSMITTING 
CIRCUIT. 


458 


DYNAMO-ELECTRIC  MACHINERY 


FIGURE  492.  —  RECEIVING 
CIRCUIT. 


high  resistance  telephones  and  produce  a  distinct  musical 
tone.  Continued  tones  are  interpreted  as  dashes  and 
I  -  short  ones  as  dots ;  together  they 

make  up  either  the  Morse  or  the 
Continental  alphabet. 

The  circuits  in  commercial 
wireless  telegraphy  are  much 
more  elaborate  than  those  shown 
(Fig.  493).  To  avoid  interfer- 
ence between  signals  from  differ- 
ent stations,  it  is  necessary  to 
tune  the  sending  and  receiving 
circuits  to  the  same  frequency. 
They  are  then  sensitive  to  one 
frequency  and  not  to  others. 
For  detailed  information  the  reader  is  advised  to  consult 
technical  books  on  wireless  telegraphy. 

567.  Uses  of  Wireless  Telegraphy.  —  In  less  than  thirty 
years  after  Hertz's  fundamental  discovery,  wireless  teleg- 
raphy has  grown  to  large  proportions,  especially  for  sig- 
nals between  ships  at  sea  and  for  international  intercourse. 
Wireless  telegraphy  is  in  use  between  all  steamships. 
They  are  thus  in  communication  with  one  another  and 
with  stations  on  the  land.  Various  government  stations 
have  been  erected  for  the  purpose  of  keeping  each  govern- 
ment in  communication  with  the  ships  in  its  navy,  and 
with  other  governments.  Notable  among  these  are  the 
station  in  Paris,  for  which  the  Eiffel  Tower  is  utilized  to 
support  the  antenna,  and  the  station  in  Arlington  near 
Washington.  Communication  between  these  two  stations 
is  not  difficult,  and  signals  between  them  have  been  used 
to  determine  the  difference  of  longitude  between  Paris 
and  Washington.  During  the  progress  of  this  work,  the 


Heinrich  Rudolf  Hertz  (1857-1894)  was  born  in  Hamburg, 
and  was  educated  for  a  civil  engineer.  Having  decided  to  aban- 
don his  profession,  he  went  to  Berlin  and  studied  under  Helm- 
holtz,  and  later  became  his  assistant.  In  1885  he  was  appointed 
professor  of  physics  at  the  Technical  High  School  at  Karlsruhe, 
and  while  there  he  discovered  the  electromagnetic  waves  pre- 
dicted by  Maxwell,  who  in  the  middle  of  the  century  had  ad- 
vanced the  idea  that  waves  of  light  are  electromagnetic  in  char- 
acter, In  1889  he  was  elected  professor  of  physics  at  Bonn, 
where  he  died  at  the  age  of  thirty-seven.  Electromagnetic  waves 
are  called  Hertzian  waves  in  his  honor. 


Thomas  Alva  Edison  was 

born  at  Milan,  Ohio,  in  1847. 
Beginning  life  as  a  newsboy, 
he  has  become  the  greatest 
American  inventor.  He  per- 
fected duplex  telegraphy, 
and  invented  among  other 
things  the  carbon  telephone 
transmitter,  the  microtasim- 
eter,  the  aerophone,  the 
megaphone,  the  phonograph, 
the  kinetoscope,  and  the  in- 
candescent electric  lamp. 


Guglielmo    Marconi   was 

born  at  Bologna,  Italy,  in 
1874.  He  studied  in  his 
native  city,  at  Leghorn,  and 
also,  for  a  short  time,  in 
England.  At  the  age  of 
twenty-one  he  began  his 
experiments  in  wireless  teleg- 
raphy, and  by  1895  was 
able  to  send  messages  across 
the  English  Channel.  Since 
then  his  system  has  been  so 
developed  that  marconigrams 
are  sent  across  the  Atlantic, 
and  practically  all  important 
ships  are  equipped  with  wire- 
less apparatus. 


WIRELESS   TELEPHONY 


459 


time  of  transmission  of  the  signals  between  Paris  and 
Washington  was  found  to  be  0.021  second.  Signals  are 
occasionally  received  at  the  Marconi  Station,  County  Gal- 
way,  Ireland,  from  stations  many  thousand  miles  away ; 
for  example,  from  Darien,  San  Francisco,  and  Honolulu. 


A.-  Aerial 

A.G.-  Anchor  Gap 

H.M.  -  Mill-Ammeter 

O.H.-  Oscillation  Helix 

R.  •  Rotary  Spark  Gap 

T.- Transformer 

C.  -  Transmitting  Condenser 

K.  •  Transmitting  Key 

G.  •  Ground 

-  Aerial  Switch 
.C.- Variable  Condenser* 
.C.  -  Loose-Coupled  Turner 

Detector 

.C.-  Fixed  Condenser 
Receivers 


FIGURE  493.  —  COMMERCIAL  TRANSMITTING  AND  RECEIVING  APPARATUS. 

568.  Wireless  Telephony.  -^-  For  the  purpose  of  trans- 
mitting speech  by  wireless,  it  is  necessary  to  have  a 
source  of  energy  that  will  transmit  a  persistent  train  of 
undamped  waves.  This  may  be  accomplished  either  by 
means  of  an  oscillating  arc  or  by  a  high  frequency  al- 
ternator. These  must  emit  continuous  trains  of  waves 
with  a  frequency  of  4000  or  more  per  second.  A  special 
microphone  carves  the  transmitted  current  and  the  train 
of  waves  emitted  into  groups  of  amplitudes  corresponding 
with  the  sounds  spoken  into  the  microphone.  The  words 
are  received  with  the  usual  telephonic  receivers. 


CHAPTER  XV 
THE   MOTOR  CAR 

569.  The  Modern  Motor  Gar  or  Automobile  has  come  into 
such  extensive  use  in  the  last  few  years  that  the  principles 
of   its   construction    and    operation   should   be  generally 
understood.     Motor  cars  are  usually  classified  according 
to  the  power  which  propels  them,  as  electric,  steam,  and 
gasoline.     Since  the  gasoline  car  is  so  much  more  widely 
used  than  either  of  the  other  two,  it  is  the  only  one  con- 
sidered in  this  chapter. 

570.  The  Gasoline  Automobile  uses  the  internal  combus- 
tion engine  (§  380),  the  four-cycle    type,  for  its  motor. 
The  number  of  cylinders  varies  from  four  to  twelve,  and 
the  pistons,  whatever    their   number,  act   on  a    common 
crank  shaft.     Figure  494  shows  a  four-cylinder  engine  and 
Figure  495   a  six.     Whatever   the  number  of  cylinders, 
the  energy  from  the  explosion  is  applied  intermittently. 
The  greater  the  number,  the  more  nearly  continuous  is 
the  stream  of  energy. 

In  the  four-cylinder  engine  there  are  two  explosions 
for  each  revolution  of  the  crank  shaft,  180°  apart.  For  a 
six,  there  are  three,  120°  apart ;  for  an  eight,  there  are 
four,  90°  apart ;  and  for  a  twelve,  there  are  six,  60°  apart. 
Figure  496  illustrates  a  twelve -cylinder  engine  or  "  twin- 
six." 

571.  The  Engine. — The  vital  part  of  the  motorcar  is 
the  engine,  and  constant  and  intelligent  attention  on  the 

460 


THE  ENGINE 


461 


Courtesy  of  Dodge  Brothers 
FIGURE  494.  —  CROSS  SECTION  OF  A  FOUR-CYLINDER  ENGINE. 


Courtesy  of  the  Buick  Company 

FIGURE  495.  —  CROSS  SECTION  OF  A  SIX-CYLINDER  VALVE-IN-HEAD  ENGINE. 


462 


THE  MOTOR   CAR 


part  of  the  operator  is  necessary  to  secure  smooth  and 
uniform  action.  In  §  380  the  mode  of  action  of  a  four- 
cycle engine  is  described,  but  if  continuous  and  uninter- 
rupted action  is  to  be  secured  a  number  of  points  must 
be  observed  :  — 

(1)   Since  the  explosion  of  the  gaseous  mixture  heats 
the  cylinder  to  a  very  high  temperature,  the  operation  of 


Courtesy  of  the  Packard  Company 

FIGURE  496.  —  ONE  SIDE  OF  A  TWELVE-CYLINDER  ENGINE. 

the  engine  soon  becomes  impossible  unless  some  cooling 
device  is  used.  This  is  secured,  except  in  the  "air- 
cooled"  type  of  car,  by  the  circulation  of  water  about  the 
cylinders  and  through  a  device  called  the  radiator,  where 
it  is  cooled  by  the  action  of  a  fan  and  the  rapid  radiation 
due  to  the  large  surface  exposed.  In  some  cases  the 
water  is  circulated  by  a  pump;  in  others,  the  so-called 
"  thermo-siphon  "  system  is  used.  By  this  system,  the 
cold  water  entering  the  water-jacket  from  the  bottom  of 


THE  ENGINE  463 

the  radiator  forces  up  the  hot  water  that  is  around  the 
cylinders  into  the  reservoir  above  the  radiator,  from 
which  it  flows  through  the  radiator  where  it  is  cooled. 


Courtesy  of  the  Cadillac  Company 
FIGURE  497.  —  FRONT  VIEW  OF  V-TYPE  ENGINE. 

Most  "  eights  "  and  "  twelves  "  are  of  this  type  with  four  or  six  cylinders 
placed  in  opposite  rows. 

The  reservoir  above  the  radiator  should  always  be  kept  as 
nearly  full  as  convenient. 

(2)   Every  motor  must  be  kept  thoroughly  lubricated. 
Practically    all    cars    now   use    both    the    "  pump "    and 


464 


THE  MOTOR  CAR 


"  splash  "  systems,  whereby  the  oil  is  not  only  spattered 
about  the  inside  of  the  engine  by  the  rapidly  revolving 
crank  shaft,  but  it  is  also  pumped  to  parts  less  likely  to  be 
reached  by  the  splash  system.  Every  engine  has  an  oil 
gauge  which  should  be  constantly  watched,  as  the  explo- 
sions of  the  gas  consume  some  of  the  oil,  and  the  absence 
of  lubricant  causes  " knocking"  and  laboring  on  the  part 
of  the  motor. 

(3)  Because  of  the  incomplete  burning  of  the  carbon  in 
the  explosion,  a  gradual  deposit  forms  on  the  pistons  and 

points  of  the  spark 
plugs.  This  accumu- 
lation of  carbon  may 
cause  a  fouling  of  the 
spark  plugs  to  such 
an  extent  that  they  do 
not  function,  and  the 
engine  stops  ;  or  it 
may  form  sufficiently 
to  hold  fire  between  ex- 
plosions, and  produce 
pre-ignition.  A  pound- 
ing or  knocking  in  the 
engine  is  one  of  the 
indications  of  the  presence  of  carbon.  It  may  be  removed 
by  opening  the  engine  and  scraping  the  carbon  off. 

(4)  The  proper  mixture  of  the  air  and  gasoline  is  neces- 
sary to  the  best  action  of  the  engine.     This  mixing  is  done 
by  the  carburetor  (Fig.  498),  a  device  through  which  the 
suction  of  the  pistons  draws  air  and  gasoline  in  proper 
proportions  for  the  several  cylinders.       The  manifold  is 
the  tube  that  conveys  the  mixture  from  the  carburetor  to 
the  different   cylinders.      Most   cars   have   a   carburetor 


FIGURE  498. 


THE  ENGINE 


465 


adjustment  on  the  dash,  so  that  any  desired  mixture  can 
be  obtained.  A  richer  mixture  is  desirable  when  starting 
the  engine  than  after  it  has  become  warm,  and  it  is  also 
possible  to  operate  on  a  thinner  mixture  at  high  speeds 
than  at  low.  A  car  which  has  been  running  satisfactorily 
at  twenty-five  miles  an  hour  on  as  thin  a  mixture  as  pos- 
sible will  often  stall  when  "  throttled  down  "  to  ten  or 
twelve  miles  an  hour.  The  carburetor  is  often  warmed 
by  a  pipe  from  the  exhaust  of  the  engine  and  sometimes 
it  is  partly  surrounded  by  a  water-jacket. 

(5)  The  gas  is  ignited  by  an  electric  spark  which 
jumps  between  two  metal  points  in  the  spark  plug,  which 
is  placed  at  or  near  the  head  of  the  cylinder.  This  spark 


SAFETY 
SPARK  GAP 


BALL  BEARING 

ARMATURE 


BALL  BEARING 


FIGURE  499.  —  DIAGRAM  OF  THE  BOSCH  MAGNETO. 

is  furnished  either  by  an  induction  coil  connected  with 
a  storage  battery  or  by  a  high-tension  magneto  (Fig. 
499)  which  is  turned  by  a  connection  with  the  crank  shaft. 
The  crank  shaft  by  suitable  gearing  also  operates  a  timer, 


466  THE  MOTOR   CAR 

which  connects  the  spark  plugs  successively  and  explodes 
the  gas  at  the  proper  time. 

Ignition  troubles  are  usually  caused  by  foul  spark 
plugs.  When  the  action  of  the  engine  is  jerky  it  shows 
that  some  cylinder  is  "missing."  The  one  at  fault  can 
be  ascertained  by  touching  some  metal  part  of  the  engine 
with  the  end  of  a  screw-driver  and  holding  another  part 
of  the  metal  of  the  screw-driver  close  to  the  spark  plug 
connections.  The  plug  where  t  no  spark  jumps  across  is 
probably  the  one  causing  the  trouble. 

572.  The  Storage  Battery.  —  So  little  attention  is  re- 
quired by  the  storage'  battery  that  it  is  often  too  much 
neglected.  It  should  be  examined  at  least  every  two 
weeks  and  the  plates  covered  with  distilled  water.  It 
should  be  tested  from  time  to  time  with  the  hydrometer 
(Fig.  60)  and  recharged  at  once  if  the  density  has  fallen 
below  1.200.  The  electrolyte  of  a  battery  in  good  condi- 
tion has  a  density  from  1.250  to  1.300.  An  idle  battery 
will  not  remain  charged  but  must  have  attention  as  often 
as  once  every  two  weeks. 

On  long  summer  trips  of  continuous  driving  and 
also  by  rapid  driving  for  a  few  hours  a  battery  some- 
times becomes  overcharged.  This  may  be  remedied  by 
switching  on  the  lights  of  the  car  for  a  while.  In  the 
winter  season,  on  account  of  the  difficulty  of  starting 
the  car  when  cold,  the  battery  is  likely  to  be  run 
down.  This  condition  will  be  accentuated  by  the  in- 
creased use  of  the  lights.  It  will  relieve  the  heavy 
drain  on  the  battery  to  start  the  car  by  the  use  of 
the  crank ;  at  least  it  is  advisable  to  turn  the  engine 
over  a  few  times  to  get  it  well  oiled  before  resorting  to 
the  starter. 


THE  RUNNING  GEAR  467 

573.  The  Chassis  (pronounced  "shassy")  is  the  name 
applied  to  the  skeleton  body  of  the  car  (Fig.  500),  as 
distinguished  from  the  hood,  which  incloses  the  engine, 
the  tonneau,  which  is  the  rear  seat  division  of  a  touring 
car,  and  the  running  gear,  as  the  wheels  are  generally 


FIGURE  500.  — A  TYPICAL  CHASSIS. 

called.  The  chief  care  required  by  the  chassis  is  its 
lubrication.  It  is  fully  supplied  with  grease  cups  which 
require  constant  "turning  up"  and  filling.  Grease 
cups  .which  lubricate  revolving  parts  require  more  fre- 
quent attention  than  those  on  joints  and  spring  bolts. 

574.  The  Running  Gear  consists  of  the  wheels  and  tires. 
The  rear  wheels  are  usually  lubricated  from  the  differen- 
tial (§  578)  and  require  practically  no  attention.  The 
bearings  of  the  front  wheels  are  usually  packed  in  grease, 
and  at  least  once  a  year  the  wheels  should  be  removed 
and  the  bearings  cleaned  and  repacked  in  grease. 

The  tires  consist  of  a  flexible  inner  tube,  containing 
air  under  pressure,  and  a  thick  outer  casing,  sometimes 
called  the  shoe.  Tire  makers  recommend  a  pressure  of 
about  twenty  pounds  for  each  inch  of  cross  sectional 
diameter;  that  is,  a  four-inch  tire  should  carry  eighty 


468  THE  MOTOR   CAB 

pounds'  pressure  to  the  square  inch ;  a  four  and  a  half, 
ninety  pounds ;  and  a  five-inch  tire,  one  hundred  pounds. 
Less  pressure  may  give  more  comfort  in  riding,  but  there 
is  the  danger  that  an  excessive  flattening  of  the  tire  may 
separate  the  layers  of  fabric  and  rubber. 

This  applies  to  the  heavy  outer  casing  wherein  lies  the 
main  expense  in  the  maintenance  of  a  car.  Oil  and  tar 
are  enemies  of  rubber  and  should  be  removed  from  the 
tire  as  soon  as  possible  by  means  of  a  cloth  dampened 
with  gasoline.  Rough  roads  should  either  be  avoided  or 
traversed  at  as  low  a  speed  as  possible.  Fast  driving, 
especially  in  hot  weather,  is  particularly  hard  on  tires  in 
that  the  tires  become  heated  and  disintegration  sets  in. 

A  blow-out  is  caused  by  a  weakening  of  the  tire  casing 
or  shoe,  through  which  the  inner  tube  is  forced  out  by 
the  air  pressure,  exploding  with  a  loud  report.  A  punc- 
ture is  caused  by  a  nail,  or  some  sharp  instrument  like  a 
piece  of  glass  cutting  through  the  casing  and  making  a 
small  hole  in  the  inner  tube,  through  which  the  air  es- 
capes gradually  without  "  blowing  out "  the  casing. 
Sometimes  a  leak  occurs  in  the  valve,  which  is  delicately 
constructed,  and  the  rubber  washer  of  which  may  be- 
come defective  through  heat  or  age.  The  valve  may 
then  be  unscrewed  by  reversing  the  little  pointed  cap 
which  protects  it  and  a  new  valve  may  be  screwed  in  at 
slight  expense. 

575.  The  Brakes.  —  All  automobiles  are  provided  with 
double  brakes  —  the  service  brake,  operated  by  the  foot, 
and  the  emergency  brake,  usually  operated  by  a  hand  lever. 
These  brakes  consist  of  steel  bands  lined  with  asbestos 
acting  by  friction  on  drums  attached  to  the  driving  shaft 
or  to  the  rear  wheels.  They  should  always  be  kept  in 


THE  CLUTCH 


469 


good  condition  and  should  always  be  applied  gradually 
except  in  a  case  of  great  emergency.  The  clutch  should 
always  be  thrown  out  when  the  brakes  are  applied.  In 
some  types  of  cars  the  clutch  and  service  brake  are  on  the 
same  foot  lever  and  in  applying  the  brake  the  construction 
is  such  that  the  clutch  is  thrown  out  before  the  brake 
comes  into  action. 

576.  The  Clutch  is  a  friction  coupling  connecting  the 
crank  shaft  with  the  transmission  shaft.  There  are  many 
different  forms,  as  the  multiple  disk,  the  cone,  etc.,  but 


FIGURE  501.  —  MULTIPLE  DISK  CLUTCH  AND  TRANSMISSION. 

those  that  have  proved  the  most  satisfactory  depend  on 
friction.  The  clutch  must  always  be  thrown  out  in  shift- 
ing the  gears  from  "  neutral,"  in  changing  the  gears  in 
any  way,  and  in  stopping  the  car,  and  it  should  be  let  in 


470  THE  MOTOR   CAR 

gently  to  prevent  jerking.     Figure  501  shows  a  section  of 
one  type  of  clutch  and  the  transmission  gears. 

577.  The  Transmission  comprises  all  those  parts  which 
transmit  power  from  the  engine  to  the  rear  wheels,  but  the 
group  of  gear  wheels  just  back  of  the  clutch  is  usually  re- 
ferred to  as  the   transmission.     Its   function   is   to   make 
changes   in  speed   possible   by   various    combinations    of 
gears.     The  gasoline  motor  develops  power  in  proportion 
to  its  speed,  so  that  if  great  pulling  power  is  required,  a 
high  speed  of  the  motor  must  be  combined  with  a  low 
speed  of  the  car,  and  this  is  obtainable  only  through  a 
system  of  gears.     In  starting  a  car  always  begin  in  low 
gear,  shifting  to  second  when  a  moderate  degree  of  speed 
has  been  attained,  and  not  going  into  "  high  "  until  the 
car  is  well  under  way. 

578.  The  Differential.  —  The  rear  wheels  of  a  car  are 
the  driving  wheels  and  motion  is  communicated  to  them 
from  the  engine  through  the  clutch,  the  transmission,  the 


FIGURE  502. — THE  DIFFERENTIAL. 


driving  shaft,  and  finally  through  a  device  called  the 
differential  (Fig.  502).  This  is  an  ingenious  assem- 
blage of  gear  wheels  so  connected  as  to  permit  the  drive 


THE  8TAETEE 


471 


wheels  to  rotate  independently,  as  is  necessary  in  turning 
a  corner.  The  differential  requires  little  attention,  but 
must  be  examined  occasionally  to  make  sure  that  it  is 
thoroughly  oiled. 

The  plan  of  the  differential  is  such  that  one  wheel  may 
turn  while  the  other  is  stationary,  and  for  this  reason  on  a 
slippery  road  it  is  necessary  to  place  a  chain  on  each  drive 
wheel.  If  only  one  chain  is  used,  the  chain  wheel  may  be 
standing  still  while  the  other  one  spins  rapidly  without 
securing  any  u  traction."  \ 

579.  The  Steering  Device  is  a  broad  wheel  and  shaft 
carrying  the  throttle  lever  and  the  spark  lever  and  connected 
with  the  front  wheels  by  an 
endless  screw  working  in  a 
worm  wheel  (Fig.  503). 
It  should  turn  readily,  but 
should  not  be  allowed  to 
have  too  much  play,  as  on 
it  depends  the  control  of 
the  car. 


580.  The  Starter.  —  Most 
cars  are  now  equipped  with 
an  electric  starter,  a  small 
direct  current  motor  oper- 
ated by  the  storage  bat- 
tery. Pressing  a  spiral 
switch  by  means  of  a  plug, 
usually  in  the  floor  board, 
closes  the  circuit,  causing 
the  armature  to  revolve.  A  suitable  reduction  gear  con- 
nects the  armature  shaft  with  the  crank  shaft  of  the 
engine,  thus  turning  it  over  and  setting  it  in  motion. 


FIGURE  503. 


472  THE  MOTOR    CAB 

Before  pressing  the  starter  plug,  the  gear  lever  should 
always  be  put  in  neutral,  the  spark  retarded,  the  throttle 
advanced,  and  the  "  mixture  "  in  the  carburetor  enriched. 
The  starting  plug  should  be  released  immediately  on  the 
engine's  beginning  to  run.  The  spark  should  then  be 
advanced,  the  motor  throttled  down  to  a  moderate  speed, 
and  the  carburetor  adjusted. 

581.  On  the  Road. — The  two  most  important  rules  of 
the  road  are  "  Safety  First "  and  •  Courtesy  to  All." 
Different  cities  and  towns  have  local  regulations,  but  the 
driver  who  is  always  careful  and  courteous  will  save  him- 
self the  trouble  of  memorizing  countless  specific  rules. 
Always  be  prepared  for  every  one  else  doing  the  wrong 
thing.  In  turning  corners  drive  slowly  and  thus  avoid 
becoming  an  example  under  §  145.  Do  not  try  to  climb 
steep  hills  on  "  high  "  just  because  you  may  be  able  to  do 
so,  and  do  not  descend  hills  at  high  speed. 

If  the  motor  stops  or  "  stalls,"  as  it  is  usually  termed, 
the  first  thing  to  investigate  is  the  gasoline  supply.  In 
nine  cases  out  of  ten  lack  of  gasoline  causes  the  stalling. 
Otherwise,  some  flaw  in  the  ignition  system,  such  as  a 
broken  wire  or  a  short  circuit,  may  cause  the  trouble. 
Sometimes  the  fan  belt  has  worked  loose  so  that  the  fan 
has  ceased  to  function  and  the  engine  is  overheated.  This 
is  usually  detected  by  the  boiling  of  the  water  in  the  water 
jacket. 

After  stopping,  it  is  best  to  set  the  emergency  brake, 
even  on  level  ground ;  but  do  not  forget  to  release  it 
before  starting.  Always  put  the  gear  lever  in  neutral  on 
stopping,  except  that  after  stopping  on  a  steep  down  grade, 
it  is  usually  wise  to  throw  the  gear  lever  into  reverse  for 
safety's  sake,  and  on  a  steep  upgrade,  to  throw  it  into  low 


THE  PEDESTRIAN  473 

gear.  But  you  should  be  particularly  careful  to  put  it 
back  into  neutral  before  attempting  to  start  the  car. 

The  engine  is  a  natural  brake.  So  in  descending  a  hill, 
throttle  the  engine  down  and  leave  the  clutch  in.  The 
speed  can  then  be  governed  easily  by  the  service  brake 
and  the  car  be  more  completely  under  control.  When  de- 
scending very  steep  hills,  it  is  well  to  go  into  second  or 
even  into  first  speed  to  brake  the  car. 

In  night  driving  do  not  use  bright  head  lights  on  ap- 
proaching another  car ;  always  turn  them  down  to  "  dim." 
A  bright  light  is  blinding  to  the  driver  of  the  oncoming 
car  and  may  cause  a  serious  accident. 

In  general,  study  the  car,  the  plan  of  all  the  parts,  their 
office,  and  their  adjustment.  Rattles  usually  come  from 
loose  nuts,  squeaks  from  empty  grease  cups.  Look  the 
car  over  often  to  see  if  everything  is  secure  and  in  place. 
Inspect  the  gasoline,  water,  and  oil  supply  before  starting 
out  from  the  garage.  In  this  way  you  will  have  fewer 
accidents  and  less  annoyance  and  expense. 

582.  The  Pedestrian.  —  In  communities  where  motor 
cars  are  numerous,  pedestrians  should  take  the  utmost 
care  to  avoid  accidents.  In  crowded  cities  which  have 
traffic  officers  at  crossings,  we  should  watch  the  signals  of 
the  officer,  keeping  on  the  sidewalk  until  he  signals  the 
traffic  to  stop. 

Where  there  is  no  officer  the  traffic  usually  keeps  to  the 
right.  Hence  we  should  look  first  to  the  left  until  halfway 
across,  then  to  the  right  for  the  rest  of  the  way.  As  we 
start  across  there  is  no  danger  of  being  hit  from  the  right; 
but  when  halfway  across,  that  is  the  side  from  which  the 
danger  comes. 

Asking  for  rides  should  be  discouraged  as  a  dangerous 


474  THE  MOTtiR   CAR 

proceeding.  If  the  driver  is  unfriendly,  we  are  completely 
at  his  mercy  and  he  can  take  us  where  he  will.  If  he  is 
friendly,  we  are  subjecting  him  to  risk,  because  he  is  liable 
for  any  injury  to  us,  whether  in  the  car  or  in  getting  on 
or  off. 

Courtesy,  common  sense,  and  obedience  to  traffic  regu- 
lations are  as  important  for  pedestrians  as  for  motorists. 


APPENDIX 


L    GEOMETRICAL  CONSTRUCTIONS 

The  principal  instruments  required  for  the  accurate  con- 
struction of  diagrams  on  paper  are  the  compasses  and  the 
ruler.  For  the  construction  of  angles  of  any  definite  size  the 

protractor  (Fig. 
504)  can  be  used. 
There  are,  how- 
ever, a  number  of 
angles,  as  90°,  60°, 
and  those  which 
can  be  obtained 
from  these  by  bi- 
secting them  and 
combining  their 

parts,  that  can  be  constructed  by  the  compasses  and  ruler  alone. 
A  convenient  instrument  for  the  rapid  construction  of  the 
angles  90°,  60°,  and  30°,  is 
a  triangle  made  of  wood, 
horn,  hard  rubber,  or  card- 
board, whose  angles  are 
these  respectively.  Such 
a  triangle  may  be  easily 
made  from  a  postal  card 
as  follows :  Lay  off  on  the 
short  side  of  the  card  (Fig. 
505)  a  distance  a  little  less 
than  the  width,  as  AB.  Separate  the  points  of  the  compasses 
a  distance  equal  to  twice  this  distance.  Place  one  point  of  the 
compasses  at  B,  and  draw  an  arc  cutting  the  adjacent  side  at  C. 

475 


90° 


FIGURE  505. 


476 


APPENDIX 


Cut  the  card  into  two  parts  along  the  straight  line  BO.  The 
part  ABC  will  be  a  right-angled  triangle,  having  the  longest 
side  twice  as  long  as  the  shortest  side,  with  the  larger  acute 
angle  60°  and  the 
smaller  30°.  With 
this  triangle  and  a 
straight  edge  the 
majority  of  the  con- 
structions required 
in  elementary  phys- 
ics can  be  made. 

PKOB.  1.  —  To  con- 
struct an  angle  of  90°. 

Let  A  be  the  ver- 
tex  of  the  required  B 
angle  (Fig.  506). 
Through  A  draw  the  straight  line  BC.  Measure  off  AD,  any 
convenient  distance  ;  also  make  AE  =  AD.  With  a  pair  of 
compasses,  using  D  as  a  center,  and  a  radius  longer  than  AD, 

draw  the  arc  mn  ;  with  E  as  a  cen- 
ter and  the  same  radius,  draw  the 
arc  rs,  intersecting  mn  at  F.  Join 
A  and  F.  The  angles  at  A  are  right 
angles. 


D 


A 

FIGURE  506. 


E 


PJBOB.  2.  —  To  construct  an  angle 
of 60°. 

Let  A  be  the  vertex  of  the  re- 
-—  quired  angle  (Fig.  507),  and  AB  one 
of  the  sides.  On  AB  take  some 
convenient  distance  as  AC.  With 
a  pair  of  compasses,  using  A  as  a  center  and  AC  as  a  radius, 
draw  the  arc  CD.  With  C  as  a  center  and  the  same  radius,  draw 
the  arc  mn,  intersecting  CD  at  E.  Through  A  and  E  draw  the 
straight  lineAE;  this  line  will  make  an  angle  of  60°  with  AB. 


C 

FIGURE  507. 


GEOMETRICAL    CONSTRUCTIONS 


477 


PROB.  3.  —  To  bisect  an  angle. 

Let  BAG  be  an  angle  that  it  is  required  to  bisect  (Fig.  508). 
Measure  off  on  the  sides  of  the  angle  equal  distances,  AD  and 

AE.  With  D  and  E  as  centers 
and  with  the  same  radius,  draw 
the  arcs  mn  and  rs,  intersecting 
at  F.  Draw  AF.  This  line 
will  bisect  the  angle  BAG. 

PROB.  4.  —  To  make  an  angle 
equal  to  given  angle. 

Let  BAG  be  a  given  angle; 

FIGURE  508  ^  *s  re(luire(l  to  make  a  second 

angle  equal  to  it   (Fig.    509). 

Draw  DE,  one  side  of  the  required  angle.  With  A  as  a  cen- 
ter and  any  convenient  radius,  draw  the  arc  mn  across  the  given 
angle.  With  D  as  a  center  and  the  same  radius,  draw  the 
arc  rs.  With  s  as  a  center  and  a  radius  equal  to  the  chord  of 


A  n  CD  E 

FIGURE  509. 

mn,  draw  the  arc  op,  cutting  rs  at  G.  Through  D  and  0- 
draw  the  line  DP.  This  line  will  form  with  DE  the  required 
angle,  as  FDE. 

PROB.  5.  —  To  draw  a  line  through  a  point  parallel  to  a 
given  line. 

Let  A  be  the  point  through  which  it  is  required  to  draw 
a  line  parallel   to   BG  (Fig.  510).      Through  A  draw   ED, 


478 


APPENDIX 


cutting  BC  at  D.     At  A  make  the  angle  EAG  equal  to  EDO. 
Then  AG  or  F#  is  parallel  to  EG. 


FIGURE  510. 


PROB.  6.  —  Given  two  adjacent  sides  of  a  parallelogram  to  com- 
plete the  figure. 

Let  AB  and  AC  be  two  adjacent  sides  of  the  parallelogram 
(Fig.  511).     With  C  as  a  center  and  a  radius  equal  to  AB, 


FIGURE  511. 

draw  the  arc  mn.  With  B  as  a  center  and  a  radius  equal  to 
AC,  draw  the  arc  rs,  cutting  mn  at  D.  Draw  CD  and  .BZ>. 
Then  ABDC  is  the  required  parallelogram. 


CONVERSION   TABLES 


479 


II    CONVERSION  TABLES 


1.   LENGTH 


To  reduce 

Multiply  by     To  reduce 

Multiply  by 

1  60935     Kilometers  to  mi.    . 

.     0.62137 

Miles  to  m  

1609.347         Meters  to  mi.      .     . 

.      0.0006214 

Yards  to  m  

.    0.91440     Meters  to  yd.      .     . 

.      1.09361 

Feet  to  m  

0  30480     Meters  to  ft.  .     .     . 

.      3.28083 

Inches  to  cm.      .     ,     . 

2.54000     Centimeters  to  in.    . 

.      0.39370 

Inches  to  mm.         .     . 

.  25.40005     Millimeters  to  iu.     . 

.     0.03937 

2.   SURFACE 

To  reduce 

Multiply  by       To  reduce 

Multiply  by 

Sq.  yards  to  m.a      .     . 

.     0.83613      Sq.  meters  to  sq.  yd. 

.     .     1.19599 

Sq.  feet  to  m  2    .     . 

0  09290      Sq  meters  to  sq.  ft 

.     .  10.76387 

Sq.  inches  to  cm.2    .     . 

.     6.45163      Sq.  centimeters  to  sq 

.  in.     0.15500 

Sq.  inches  to  mm.2 

645.163          Sq.  millimeters  to  sq. 

in.     0.00166 

- 

3.   VOLUME 

To  reduce 

Multiply  by      To  reduce 

Multiply  by 

Cu.  yards  to  m.8      .     . 

0.76456      Cu.  meters  to  cu.  yd. 

.     .     1.30802 

Cu.  feet  to  m.3    . 

0  02832      Cu  meters  to  cu  ft 

.     .  35.31661 

Cu.  inches  to  cm.3  . 

.  16.38716      Cu.  centimeters  to  cu 

.  in.     0.06102 

Cu.  feet  to  liters      .     . 

.  28.31701      Liters  to  cu.  ft.  .     . 

.     .     0.03532 

Cu.  inches  to  liters 

.    0.01639      Liters  to  cu.  in. 

.     .  61.02337 

Gallons  to  liters  .    .     . 

.     3.78543      Liters  to  gallons      . 

.     .    0.26417 

Pounds  of  water  to  liters 

.    0.45359     Liters  of  water  to  Ib. 

.    2.20462 

4.   WEIGHT 

To  reduce 

Multiply  by      To  reduce 

Multiply  by 

Tons  to  kg  

907.18486      Kilograms  to  tons 

0.001102 

Pounds  to  kg.       .     .     . 

0.45359      Kilograms  to  Ib.      . 

2.20462 

Ounces  to  g  

28.34953      Grams  to  oz.       .     . 

0.03527 

Grains  to  g. 

0.064799      Grams  to  grains 

15.4323B 

480 


APPENDIX 


5.  FORCE,  WORK,  ACTIVITY,  PRESSURE 


To  reduce  Multiply  by 

Lb.-weight  to  dynes,  .  444520.58 
Ft.-lb.  to  kg.-m.  .  .  .  0.138255 
Ft.-lb.  to  ergs  .  .  13549  x  108 
Ft.-lb.  to  joules  .  .  1.3549 

Ft.-lb.  per  sec.  to  H.P.  18182  x  10~7 
H.P.  to  watts  ....  745.196 
Lb.  per  sq.  ft.  to  kg. 

perm.2 4.8824 

Lb.  per  sq.  in.  to  g. 

per  cm.2 70.3068 

Calculated  for  g  =  980  cm. , 


To  reduce  Multiply  bj 

Dynes  to  Ib. -weight,  22496  x  10'10 
Kg.-m.  to  ft.-lb.  .  .  .  7.233 
Ergs  to  ft.-lb.  .  .  0-7381  x  10~7 
Joules  to  ft.-lb.  ...  0.7381 
H.P.  to  ft.-lb.  per  sec.  .  550 

Watts  to  H.P 0.001342 

Kg.  per  m.2  to  Ib.  per 

sq.  ft 0.2048 

G.  per  cm.2  to  Ib.  per 

sq.  in 0.01422 

or  32.15  ft.-per-sec.  per  sec. 


6.   MISCELLANEOUS 


To  reduce  Multiply  by 

Lb.  of  water  to  U.S.  gal.  0. 11983 

Cu.  ft.  to  U.S.  gal.  .  .  7.48052 
Lb.  of  water  to  cu.  ft.  at 

4°C 0.01602 

Cu.  in.  to  U.S.  gal.  .  .  0.004329 
Atmospheres  to  Ib.  per 

sq.  in 14.69640 

Atmospheres  to  g.  per 

cm.2 1033.296 

Lb.-degrees  F.  to  calories.  252 

Calories  to  joules  .  .  .  4.18936 
Miles  per  hour  to  ft.  per 

sec 1.46667 

Miles  per  hour  to  cm.  per 

sec.  ,                           .  44.704 


To  reduce  Multiply  by 

U.S.  gal.  to  Ib.  of  water.  8.345 

U.S.  gal.  to  cu.  ft.       .     -  0.13368 

Cu.  ft.  of  water  at  4°  C. 

tolb 62.425 

U.S.  gal.  to  cu.  in.      .     .  231 

Lb.  per  sq.  in.  to  atmos- 
pheres   0.06737 

G.  per  cm.2  to  atmos- 
pheres    0.000968 

Calories  to  Ib. -degrees  F.  0.003968 

Joules  to  calories  .     .     .  0.2387 

Ft.  per  sec.  to  miles  per 

hour 0.68182 

Cm.  per  sec.  to  miles  per 

hour  0.02237 


MENSURATION    TABLES 


481 


MENSURATION  RULES 


Area  of  triangle 
Area  of  triangle 
Area  of  parallelogram 
Area  of  trapezoid 
Circumference  of  circle      : 

Diameter  of  circle  • 

Area  of  circle  . 

Area  of  ellipse 
Area  of  regular  polygon 
Lateral  surface  of  cylinder 
Volume  of  cylinder 

Surface  of  sphere  : 

Volume  of  sphere  : 

Surface  of  pyramid  •> 
Surface  of  cone  I 
Volume  of  cone 


=  £  (base  x  altitude). 


V«(«—  <*)(*—  &)(*—  c)  where  s=|  (a+6+e). 
base  x  altitude. 

Altitude  x  ^  sum  of  parallel  sides.  dLJj 
diameter   x  3.1416. 

t  circumference  -f-  3.1416. 

I  circumference  x  0.3183. 

f  diameter  squared  x  0.7854. 
\  radius  squared  x  3.1416.       ^  <3.« 
product  of  diameters  x  0.7854. 
\  (sum  of  sides  x  apothem). 
circumference  of  base  x  altitude. 
=  area  of  base  x  altitude. 

(  diameter  x  circumference. 
\4  x  3.1416  x  square  of  radius. 

f  diameter  cubed  x  0.5236. 
"  I  f  of  radius  cubed  x  3.1416. 
=  $  (circumference  of  base  x  slant  height). 

=  J  (area  of  base  x  altitude). 


482 


APPENDIX 


IV.  TABLE  OF  DENSITIES 

The  following  table  gives  the  mass  in  grams  of  1  cm.8  of  the  sub- 
stance :  — 


Agate     .......  2.615 

Air,  at  0°  C.  and  76  cm. 

pressure 0.00129 

Alcohol,  ethyl,  90%,  20°  C.  0.818 

Alcohol,  methyl  .    ..    ,-,    .  0.814 

Alum,  common    ...     .  1.724 

Aluminum,  wrought     .     .  2.670 

Antimony,  cast   .    V.     .  6.720 

Beeswax 0.964 

Bismuth,  cast      ...--.     .  .9.822 

Brass,  cast      .     .  .  8.400 

Brass,  hard  drawn    .     .     .  8.700 

Carbon,  gas    .....  1.89 

Carbon  disulphide    .     .     .  1.293 

Charcoal 1.6 

Coal,  anthracite  .     .1.23  to  1.800 

Coal,  bituminous     .   1.-J7  to  1.423 

Copper,  cast 8.830 

Copper,  sheet 8.878 

Cork 0.14  to  0.24 

Diamond 3.530 

Ebony 1.187 

Emery 3.900 

Ether     .......  0.736 

Galena 7.580 

German  silver      ....  8.432 

Glass,  crown 2.520 

Glass,  flint      ...    3.0  to  3.600 

Glass,  plate 2.760 

Glycerin 1.260 

Gold       . 19.360 

Granite.     ......  2.650 

Graphite 2.500 

Gypsum,  crys.     ,    ,     ,     ,  2.310 


Human  body    ....  0.890 
Hydrogen,  at.  0°  C.  and 

76  cm.  pressure      .     .  0.000080C 

Ice 0.917 

Iceland  spar     .     .     .     .  2.723 

India  rubber    ....  0.930 

Iron,  white  cast    .     .     .  7.655 

Iron,  wrought  ....  7.698 

Ivory .     .     ......     .     1.820 

Lead,  cast   .    Y    .     .     .  11.360 
Magnesium       ....     1.750 

Marble 2.720 

Mercury,  at  0°  C.       .     .  13.596 
Mercury,  at  20°  C.     .     .13.558 

Milk 1.032 

Nitrogen,  at  0°  C.   and 

76  cm.  pressure      .     .  0.001255 

Oil,  olive 0.915 

Oxygen,  at  0°  C.  and  76 

cm.  pressure      .     .     .     0.00143 
Paraffin  .     .     .     0.824  to  0.940 

Platinum 21.531 

Potassium 0.865 

Silver,  wrought     .     .     .  10.56 

Sodium 0.970 

Steel 7.816 

Sulphuric  Acid      .     .     .     1.84 

Sulphur 2    33 

Sugar,  cane      ....     1.5. 

Tin,  cast 7.290 

Water,  at  0°  C.     .     .     .     0.999 
Water,  at  20°  C.  .     .     .     0.998 

Water,  sea 1.027 

Zinc,  cast 7.000 


GEOMETBICA  L    CONS  TB  UCTION 


483 


V.    GEOMETRICAL  CONSTRUCTION  FOR  REFRACTION 
OF  LIGHT 

• 
The  path  of  a  ray  of  light  in  passing  from  one  medium  into 

another  of  different  optical  density  is  easily  constructed  geomet- 
rically.   The  following  problems  will  make  the  process  clear : 

First. — A  ray  from  air  into  water.  —  Let  JOT"  (Fig.  502)  be 
the  surface  separating  air  from  water,  AB  the  incident  ray  at 
B,  and  BE  the  normal.  With  B  as  a  eenter  and  a  radius  BA 

draw  the  arcs  mn  and  Cs.  With 
the  same  center  and  a  radius  f  of 
AB,  (^  being  the  index  for  air  to 
water),  draw  the  arc  Dr.  Produce 
AB  till  it  cuts  the  inner  arc  at  D. 
Through  D  draw  DC  parallel  to 
the  normal  EF,  cutting  the  outer 
arc  at  0.  .Draw  BC.  This  will 
be  the  refracted  ray,  because 

—  =  -,  the  index  of  refraction. 

When  the  ray  passes  from  a 
medium  into  one  of  less  optical 
density,  then  the  ray  is  produced 
until  it  cuts  the  outer  or  arc  of 
larger  radius,  and  a  line  is  drawn  through  this  point  parallel 
to  the  normal.  The  intersection  of  this  line  with  the  inner  arc 
gives  a  point  in  the  refracted  ray  which  together  with  the 
point  of  incidence  locates  the  ray. 

If  the  incident  angle  is  such  that  this  line  drawn  parallel  to 
the  normal  does  not  cut  the  inner  arc,  then  the  ray  does  not 
pass  into  the  medium  at  that  point  but  is  totally  reflected  as 
from  a  mirror. 

It  is  immaterial  whether  the  arcs  Dr  and  Cs  are  drawn  in 
the  quadrant  from  which  the  light  proceeds,  or,  as  in  the 
figure,  in  the  quadrant  toward  which  it  is  going. 


FIGURE  512. 


484 


APPENDIX 


Second. —  Tracing  a  ray  through  a  lens.  —  Let  MN  represent 
a  lens  whose  centers  of  curvature  are  C  and  C",  and  AB  the 
ray  to  be  traced  through  it  (Figs.  503,  504).  Draw  the  normal, 


FIGURE  513. 

OB,  to  the  point  of  incidence.  With  B  as  a  center,  draw  the 
arcs  mn  and  rs,  making  the  ratio  of  their  radii  equal  the  index 
of  refraction,  f .  Through  p,  the  intersection  of  AB  with  rs, 
draw  op  parallel  to  the  normal,  OB,  and  cutting  mn  at  o. 
Through  o  and  B  draw  oBD;  this  will  be  the  path  of  the  ray 
through  the  lens. 
At  D  it  will  again 
be  refracted ;  to 
determine  the 
amount,  draw  the 
normal  CD  and 
the  auxiliary  cir- 
cles, xy  and  uv,  as 
before.  Through 
the  intersection  of  BD  produced  with  xy,  draw  It  parallel  to 
the  normal  CD,  cutting  uv  at  I.  Through  D  and  I  draw  DH-, 
this  will  be  the  path  of  the  ray  after  emergence. 

When  the  index  of  refraction  is  f ,  the  principal  focus  of  both 
the  double  convex  and  the  double  concave  lens  is  at  the  center 
of  curvature ;  for  piano-lenses,  it  is  at  twice  the  radius  of 
vature  from  the  lens. 


N 
FIGURE  514. 


INDEX 


[References  are  to  pages.] 


Aberration,          chromatic,         264 ; 

spherical,  235,  253. 
Absolute,     scale     of     temperature, 

293  ;  unit  of  force,  105  ;  zero,  294. 
Absorption  spectra,  268. 
Accelerated  motion,  95. 
Acceleration,  93;    centripetal,  100; 

of  gravity,  124. 
Achromatic  lens,  265. 
Action  of  points,  347. 
Adhesion,  10;  selective,  11. 
Agonic  line,  338. 
Air,   brake,   87 ;    compressibility  of, 

73  ;    compressor,  76  ;    pressure  of, 

68  ;   weight  of,  65. 
Air  brake,  87. 
Air  columns,  laws  of,  206. 
Airplane,  3,  113,  120,  325. 
Air   pump,    76;     experiments   with, 

78. 

Airships,  81. 
Alternator,  431. 
Altitude  by  barometer,  71. 
Ammeter,  397. 
Ampere,  381. 
Amplitude,  138. 
Analysis  of  light,  263. 
Aneroid  barometer,  70. 
Annealing,  15. 
Anode,  373. 
Antinode,  204. 
Arc,    carbon,    442;     inclosed,    443; 

open,  443. 

Archimedes,  principle,  53. 
Armature,  421,  425;  drum,  425. 
Artesian  well,  50. 


Athermanous  substances,  318. 
Atmosphere,  unit  of  pressure,  69. 
Atmospheric  electricity,  358. 
Attraction,  electrical,  340;    molecu- 
lar, 30,  35. 
Audion,  456. 
Aurora,  360. 
Automobiles,  1,  325,  460-474. 

Balance,  163. 

Balloons,  80. 

Barometer,  aneroid,  70;  mercurial, 
69  ;  utility  of,  70. 

Baroscope,  80. 

Battery,  storage,  376;  in  a  motor 
car,  466. 

Beam  of  light,  216. 

Beats,  195  ;  number  of,  196. 

Bell,  electric,  449. 

Binocular,  prism,  262. 

Blind  spot,  261. 

Blow-out,  of  a  tire,  468. 

Boiling,  303  ;   in  a  motor  car,  472. 

Boiling  point,  effect  of  pressure, 
305  ;  on  thermometer,  283. 

Boyle's  law,  74  ;    inexactness  of,  75. 

Brake,  of  a  motor  car,  468 ;  use  of 
engine  as,  473. 

Bright  line  spectra,  268. 

British  "tank,"  2,  104. 

Brittleness,  14. 

Buoyancy,  53;  of  air,  80;  meas- 
ure of,  53. 

Caloric,  280. 
Calorie,  297. 


INDEX 


[References  are  to  pages.] 


Camera,  photographer's,  259. 

Capacity,  dielectric,  352;  electro- 
static, 350 ;  thermal,  297. 

Capillarity,  32;  laws  of,  33;  re- 
lated to  surface  tension,  34. 

Capstan,  165. 

Carbon,  in  a  motor  car,  464. 

Carburetor,  464. 

Cartesian  diver,  56. 

Cathode,  373  ;  rays,  412. 

Caustic,  236. 

Cell,  voltaic,  361 ;  chemical  action 
in,  363. 

Center,  of  gravity,  123 ;  of  oscilla- 
tion, 139 ;  of  percussion,  140 ;  of 
suspension,  138. 

Centrifugal  force,  133;  illustra- 
tions of,  135  ;  its  measure,  134. 

Centripetal  force,  133. 

Charge,  residual,  353 ;  seat  of, 
353. 

Charles,  law  of,  293. 

Chassis,  of  a  motor  car,  467. 

Choke  coil,  436. 

Chord,  major,  197 ;   minor,  197. 

Chromatic  aberration,  264. 

Circuit,  closing  and  opening,  363 ; 
divided,  397  ;  electric,  363  ;  trans- 
mitting and  receiving,  457. 

Circular  motion,  100. 

Clarinet,  205. 

Clinical  thermometer,  285. 

Clutch,  of  a  motor  car,  469. 

Coherer,  455. 

Cohesion,  10. 

Coil,  choke,  436;  induction,  406; 
primary,  406.;  secondary,  407. 

Cold  by  evaporation,  303. 

Color,  271 ;  complementary,  275  ; 
mixing,  273;  of  opaque  bodies, 
271 ;  of  transparent  bodies,  272  ; 
primary,  273. 

Commutator,  423. 

Composition  of  forces,  107;  of 
velocities,  113. 


Compressibility  of  air,  73. 

Concave,  lens,  249;  mirror,  229; 
focus  of,  230,  249. 

Condenser,  351 ;  office  of,  408. 

Conductance,  of  electricity,  378 ; 
of  heat,  309. 

Conductor,  electrical,  343 ;  charge 
on  outside,  346 ;  magnetic  field 
about,  387. 

Cone  clutch,  469. 

Conservation  of  energy,  153. 

Convection,  312 ;   in  gases,  313. 

Convex,  lens,  246 ;  mirror,  231 ; 
focus  of,  230. 

Cooling  system,  in  a  motor  car,  462, 
463. 

Coulomb,  348. 

Couple,  109. 

Crank  shaft,  in  a  motor  car,  460. 

Critical  angle,  244. 

Crookes  tubes,  412. 

Crystal  detectors,  455. 

Crystallization,  35. 

Current,  electric,  361 ;  convection, 
313;  detection  of,  366;  heating 
effects  of,  385;  induced  by  cur- 
rents, 403  ;  induced  by  magnets, 
402  ;  magnetic  properties  of,  387  ; 
mutual  action  of,  390 ;  strength 
of,  381. 

Curvilinear  motion,  99. 

Cyclonic  storms,  71. 

Cylinders,  in  a  motor  car,  460-463. 

Daniell  cell,  370. 
Day,  sidereal,  23  ;  solar,  22. 
Declination,  magnetic,  338. 
Density,  58 ;    of  a  liquid,  62 ;    of  a 

solid,  60 ;  bulb,  62. 
Derrick,  165. 
Deviation,  angle  of,  241. 
Dew  point,  307. 
Diamagnetic  body,  328. 
Diathermanous  body,  318. 
Diatonic  scale,  197. 


INDEX 


[References  are  to  pages,} 


Dielectric,  351 ;  capacity,  352 ;  in- 
fluence of,  351. 

Differential,  in  a  motor  car,  467, 
470,  471. 

Diffraction,  278. 

Diffusion,  25,  28. 

Dipping  needle,  337. 

Discharge,  intermittent,  411 ;  oscil- 
latory, 453. 

Dispersion,  263. 

Drum  armature,  425. 

Dry  cell,  371. 

Dry  dock,  57. 

Dryness,  307. 

Ductility,  12. 

Dynamo,  421 ;  compound,  426 ; 
series,  425  ;  shunt,  425. 

Dyne,  105. 

Earth,  a  magnet,  336. 

Ebullition,  303. 

Echo,  186. 

Efficiency,  159. 

Effusion,  26. 

Elasticity,  36;  limit  of,  36;  of 
form,  36 ;  of  volume,  36. 

Electric,  bell,  449;  circuit,  363; 
current,  361 ;  current  detection, 
366;  motor,  426;.  railways,  430; 
telegraph,  447  ;  waves,  454. 

Electrical,  attraction,  340;  distri- 
bution, 346 ;  machines,  355 ; 
potential,  348 ;  repulsion,  341 ; 
resistance,  378  ;  wind,  347. 

Electrification,  340 ;  atmospheric, 
358;  by  induction,  344;  kinds 
of,  341 ;  simultaneous,  342 ;  unit 
of,  348. 

Electrode,  363,  377. 

Electrolysis,  373  ;  laws  of,  375 ;  of 
copper  sulphate,  373 ;  of  water,  374. 

Electrolyte,  362,  373. 

Electromagnet,  392 ;  applications 
of,  394. 

Electromotive  force,  365,  381 ;    in- 


duced by  magnets,  401 ;    induced 

by  currents,  403. 
Electrons,  419. 
Electrophorus,  354. 
Electroplating,  376. 
Electroscope,  342. 

Electrostatic,     capacity,     350;      in- 
duction, 344. 
Electrostatics,  340. 
Electrotyping,  376. 
Energy,    1,    148;     conservation    of, 

153  ;   dissipation  of,  153  ;   kinetic, 

150 ;   measure  of,  151 ;    potential, 

149  ;   transformation  of,  152. 
Engine,     gas,     323;      steam,     320; 

two-cycle,    325;     four-cycle,   324, 

460-466. 
'English    system    of    measurement, 

22. 

Equilibrant,  109. 
Equilibrium,    108;     kinds   of,    125; 

of    floating    bodies,    55 ;      under 

gravity,  125. 
Erg,  145. 
Ether,  214. 

Evaporation,  cold  by,  303. 
Expansion,      coefficient      of,      289; 

of  gases,  289  ;   of  liquids,  288 ;   of 

solids,  287. 
Extension,  6. 
Eye,  259  ;  defects  of,  262. 

Falling  bodies,  128,  130. 

Field,  electrical,  387,  391 ;  mag- 
netic, 333. 

Field  magnet,  425. 

Floating  bodies,  55. 

Fluids,  39;  characteristics  of,  39; 
pressure  in,  41. 

Fluoroscope,  415. 

Flute,  205. 

Focus,  230;  conjugate,  232;  of 
lens,  249  ;  of  mirrors,  232. 

Foot,  18. 

Foot  pound,  144. 


INDEX 


[References  are  to  pages.} 


Force,  5,  104  ;  composition  of,  107 ; 
graphic  representation  of,  107 ; 
how  measured,  106 ;  molecular, 
29 ;  moment  of,  160 ;  parallelo- 
gram of,  110;  resolution  of,  111; 
units  of,  105. 

Force  pump,  86. 

Forced  vibrations,  188. 

Fountain,  siphon,  85 ;   vacuum,  79. 

Four-cylinder  engine,  460,  461. 

Fraunhofer  lines,  268. 

Freezing,  mixtures,  302 ;  point,  283. 

Friction,  156 ;  uses  of,  158,  469. 

Fundamental,  tone,  202  ;  units,  23. 

Fusion,  299;  heat  of,  301. 

Gallon,  20. 

Galvanometer,  d'Arsonval,  395. 

Galvanoscope,  366. 

Gas  engine,  322-325,  460-466. 

Gas  equation,  294. 

Gases,  40 ;  compressibility  of,  41 ; 
expansion  of,  289;  media  for 
sound,  182  ;  thermal  conductivity 
of,  310. 

Gassiot's  cascade,  410. 

Gauge,  water,  49. 

Geissler  tube,  410. 

Grades,  170. 

Grain,  21. 

Gram,  21. 

Gramme  ring,  424. 

Gravitation,  122  ;   law  of,  123. 

Gravitational  unit  of  force,  105. 

Gravity,  122 ;  acceleration  of,  122 ; 
cell,  371 ;  center  of,  123 ;  direc- 
tion of,  122  ;  specific,  59. 

Hammer,  riveting,  88. 

Hardness,  14. 

Harmonic,  curve,  178 ;  motion, 
101. 

Harmonics,  204. 

Heat,  280 ;  conduction  of,  309  ;  con- 
vection of,  312 ;  due  to  electric 
current,  385;  from  mechanical 


action,  319;  kinetic  theory  of, 
280;  lost  in  solution,  302;  me- 
chanical equivalent  of,  320; 
measurement  of,  297 ;  nature  of, 
280 ;  of  fusion,  301 ;  of  vaporiza- 
tion, 306;  radiant,  315;  related 
to  work,  319;  specific,  297; 
transmission  of,  309. 

Heating  by  hot  water,  312. 

Helix,  389  ;   polarity  of,  389. 

Holtz  machine,  355. 

Hooke's  law,  37. 

Horizontal  line  or  plane,  123. 

Horse  power,  147. 

Humidity,  307. 

Hydraulic,  elevator,  44;  press,  42; 
ram,  51. 

Hydro-airplanes,  cuts  facing  page  66. 

Hydrometer,  63,  466. 

Hydrostatic  paradox,  47. 

Ice  plant,  ammonia,  304. 

Images,  by  lenses,  250 ;  by  mirrors, 
225,  233  ;  by  small  openings,  218. 

Impenetrability,  6. 

Impulse,  116. 

Incandescent  lamp,  444. 

Inclination,  387. 

Inclined  plane,  169;  mechanical 
advantage  of,  170. 

Index  of  refraction,  240. 

Indicator  diagram,  322. 

Induced  magnetism,  331. 

Induction,  charging  by,  345 ;  coil, 
406  ;  electromagnetic,  401 ;  elec- 
trostatic, 344  ;  motors,  440  ;  self- 
induction,  405. 

Inertia,  7. 

Influence  machine,  355. 

Insulator,  343. 

Intensity  of  illumination,  219. 

Interference,  of  light,  276;  of 
sound,  194. 

Intervals,  196 ;  of  diatonic  scale, 
198';  of  tempered  scale,  199. 


INDEX 


[References  are  to  pages.] 


Ions,  364. 
Isobars,  71. 
Isoclinic  lines,  337. 
Isogonic  lines,  338. 

Joseph  Henry's  discovery,  405. 

Joule,  145. 

Joule's  equivalent,  320 ;  law,  385. 

Kaleidoscope,  229. 

Keynote,  197. 

Kilogram,  21. 

Kilogram  meter,  144. 

Kinetic   energy,    150;    measure  of, 

151. 
Kinetic  theory,  27  ;  of  heat,  280. 

Lag  of  current,  433. 

Lalande  cell,  372. 

Lamp,  arc,  442;  gas-filled,  446; 
incandescent,  444 ;  metal  fila- 
ment, 445. 

Lantern,  projection,  259. 

Law,  Boyle's,  74;  Lenz's,  404; 
Ohm's,  378;  of  Charles,  293;  of 
electromagnetic  induction,  401 ; 
of  electrostatic  action,  342 ;  of 
falling  bodies,  130 ;  of  gravita- 
tion, 123  ;  of  heat  radiation,  316  ; 
of  magnetic  action,  330 ;  of  ma- 
chines, 156 ;  Pascal's,  41. 

Laws,  of  motion,  117;  of  strings, 
201. 

Leclanche  cell,  371. 

Length,  17. 

Lens,  246  ;  achromatic,  265  ;  focus 
of,  248  ;  images  by,  250. 

Lenz's  law,  404. 

Lever,  161 ;  mechanical  advantage 
of,  162. 

Leyden  jar,  352;  theory  of,  353; 
charging  and  discharging,  352. 

Lift  pump,  85. 

Light,  214;  analysis  of,  263; 
propagation  of,  216 ;  reflection 


of,  223  ;  refraction  of,  238 ;  speed 
of,  215 ;  synthesis  of,  264. 

Lightning,  358 ;  rod,  359. 

Lines,  agonic,  338 ;  isoclinic,  337 ; 
of  magnetic  force,  333. 

Liquefaction,  299. 

Liquid,  4,  40;  cohesion  in,  11; 
compressibility  of,  40;  density 
of,  62 ;  downward  pressure,  45 ; 
expansion  of,  288;  in  connected 
vessels,  49 ;  medium  for  sound, 
182  ;  surface  level  in,  49 ;  surface 
tension  in,  30 ;  thermal  con- 
ductivity of,  310;  velocity  of 
sound  in,  185. 

Liter,  20. 

Local  action,  367. 

Lodestone,  327. 

Longitudinal  vibrations,  177. 

Loudness  of  sound,  192. 

Lubrication,  of  a  motor  car,  463,  464. 

Machine,    155;    efficiency   of,    159; 

electrical,     355;      law     of,     156; 

mechanical    advantage    of,    160; 

simple,  159. 

Magdeburg  hemispheres,  79. 
Magnet,   artificial,  328;    bar,  328; 

electro-,     392;     horseshoe,     328; 

natural,  327. 
Magnetic,   action,   330;    axis,   329; 

field,    333;     lines   of   force,    333; 

meridian,       329;     needle,       329; 

polarity,    329;     substance,    328; 

transparency,  329. 
Magnetism,   induced,    330 ;     nature 

of,  332 ;  permanent  and  tem- 
porary, 332;  terrestrial,  336; 

theory  of,  333. 

Magneto,  in  a  motor  car,  465. 
Magnets,  327. 
Major  chord,  197. 
Malleability,  14. 
Manifold,  in  a  motor  car,  464. 
Manometric  flame,  209. 


6 


INDEX 


[References  are  to  pages.] 


Mass,  9;  units  of,  2l. 

Matter,  1 ;    properties  of,  6 ;    states 

of,  4. 

Mechanical  advantage,  160. 
Mechanical     equivalent     of     heat, 

320. 
Mechanics,  of  fluids,  39 ;    of  solids, 

104. 
Melting     point,     299;      effect     of 

pressure,  301. 
Meter,  17. 
Metric  system,  17. 
Micrometer,  174. 
Microphone,  451. 

Microscope,  compound,  256;    sim- 
ple, 255. 

Minor  chord,  197. 
Mirror,  225  ;   focus  of,  230 ;    images 

by,       226,       233;     plane,       225; 

spherical,  229. 
Mobility,  39. 
Molecular,     forces,     29 ;      motion, 

26 ;   physics,  25. 
Moment,  of  a  force,  160. 
Momentum,  116. 
Motion,       91 ;       accelerated,       95 ; 

curvilinear,   99 ;    harmonic,    101 ; 

molecular,     26 ;      periodic,     101 ; 

rectilinear,      91 ;       rotary,      91 ; 

uniform,  92;   vibratory,   101. 
Motor,     electric,     426 ;      induction, 

440. 

Motor  car,  1,  460-474. 
Multiple-disk  clutch,  469. 
Musical,  scales,  196 ;  sounds,  191. 

Needle,    dipping,    337 ;     magnetic, 

329. 
Newton's,    laws    of    motion,     116; 

rings,  276. 
Nodes,  203. 
Noise,  191. 

Octave,  197. 

Ohm's  law,  378,  382. 


Opaque  bodies,  214. 
Opera  glasses,  258. 
Optical,  center,  247;  instruments, 

255. 

Organ  pipe,  206. 
Oscillation,  center  of,  139  ;   electric, 

360. 

Ounce,  22. 
Overtones,  204,  208. 

Partial  tones,  204. 

Pascal,  experiments,  67;    principle, 

41. 
Pendulum,     applications     of,     140; 

laws     of,     138;      seconds,      141; 

simple,  136. 

Percussion,  center  of,  140. 
Period  of  vibration,  138. 
Periodic  motion,  101. 
Permeability,  335. 
Phonodeik,  211. 
Photographer's  camera,  259. 
Photometer,  221. 
Photometry,  219. 
Physical  measurements,  16. 
Physics,  1. 
Pigments,  275. 
Pistons,  in  a  motor  car,  460. 
Pitch,  191 ;   limits  of,  199 ;    relation 

to  wave  length,    192 ;    of   screw, 

173. 

Plumb  line,  123. 
Pneumatic  appliances,  83. 
Points,  action  of,  347. 
Polarity  of  helix,  389. 
Polarization,  368. 
Polyphase  alternators,  434. 
Porosity,  11. 
Potential,     difference,     348;      zero, 

349. 

Pound,  21. 
Power,  145. 
Pre-ignition,  464. 
Pressure,   41 ;    of  fluids,   39 ;    at  a 

point  in  fluids,  46  ;  air,  65  ;  down- 


INDEX 


[References  are  to  pages.] 


ward,  45 ;  effect  on  boiling  point, 
305  ;  effect  on  melting  point,  301 ; 
independent  of  shape  of  vessel,  47 ; 
in  tires,  467. 

Principle  of  Archimedes,  53. 

Prism,  242  ;  angle  of  deviation,  243. 

Proof  plane,  342. 

Properties  of  matter,  6. 

Pulley,  165;  differential,  168;  me- 
chanical advantage  of,  167  ;  sys- 
tems of,  166. 

Pump,  air,  76 ;  compression,  76 ; 
force,  86 ;  lift,  85. 

Puncture,  of  a  tire,  468. 

Quality  of  sounds,  193;  due  to 
overtones,  193. 

Radiation,  315  ;   laws  of,  316. 

Radiator,  in  a  motor  car,  462. 

Radioactivity,  416. 

Radiometer,  315. 

Radium,  417. 

Rainbow,  266. 

Rays  of  light,  216. 

Reflection,  diffused,  224;  law  of, 
223;  multiple,  228;  of  light, 
223 ;  of  sound,  186 ;  regular, 
223  ;  total,  243. 

Refraction,  cause  of,  239 ;  atmos- 
pheric, 243  ;  laws  of,  241. 

Regelation,  301. 

Relay,  448. 

Resistance,  of  air,  129 ;  electrical, 
378;  formula  for,  380;  laws  of, 
379  ;  unit  of,  379. 

Resolution,  of  a  force,  111;  of  a 
velocity,  113. 

Resonance,  188,  190. 

Resonator,  Helmholtz's,  191. 

Resultant,  107. 

Riveting  hammer,  88. 

Roentgen  rays,  414. 

Rotating  field,  438. 

Running  gear,  of  a  motor  car,  467, 
468. 


Scale,  absolute,  293;  diatonic, 
197 ;  tempered,  198. 

Screw,  172;  applications  of,  173; 
mechanical  advantage  of,  173. 

Second,  22. 

Secondary  or  storage  cell,  376. 

Seconds  pendulum,  141. 

Self-induction,  405. 

Shadows,  217. 

Shoe,  in  a  motor  car,  467 

Sidereal  day,  23. 

Sight,  260. 

Singing  flame,  195. 

Siphon,  83  ;   intermittent,  85. 

Six-cylinder  engine,  460,  461. 

Solar  day,  22. 

Solenoid,  389  ;   polarity  of,  389. 

'Solids,  4;  density  of,  60;  ex- 
pansion of,  287 ;  thermal  con- 
ductivity of,  309 ;  velocity  of 
sound  in,  185. 

Solution,  34 ;  saturated,  35 ;  heat 
lost  in,  302. 

Sonometer,  201. 

Sound,  176,  181 ;  air  as  a  medium, 
182;  liquids  as  media,  182; 
loudness  of,  192 ;  musical,  191 ; 
quality  of,  193 ;  reflection  of, 
186 ;  sources  of,  181 ;  trans- 
mission of,  182 ;  velocity  of, 
184 ;  waves,  183. 

Sounder,  telegraph,  447. 

Spark  lever,  471. 

Spark  plug,  465. 

Specific  gravity,  59  ;   bottle,  62. 

Specific  heat,  297. 

Spectroscope,  269. 

Spectrum,  solar,  263;  kinds  of, 
268. 

Speed,  92  ;   of  light,  215. 

Speeds,  of  a  motor  car,  470. 

Spherical  aberration,  in  mirrors, 
235  ;  in  lenses,  253. 

Spheroidal  state,  303. 

Spherometer,  174. 


INDEX 


[References  are  to  pages.] 


Splash  system,  of  lubrication,  464. 

Stability,  126. 

Stable  equilibrium,  125. 

Stalling,  of  a  gas  engine,  472. 

Starter,  in  a  motor  car,  471. 

Starting  resistance,  429. 

States  of  matter,  4. 

Steam,  engine,  320 ;  turbine,  322. 

Steelyard,  162. 

Storage  cell,  376,  466;  Edison,  378. 

Strain,  36. 

Strength,    of   an    electric     current, 

381 ;  methods  of  varying,  383. 
Stress,  36. 

Strings,  laws  of,  201. 
Sublimation,  303. 
Submarine  boat,  57. 
Surface    tension,    30;     illustrations 

of,  31. 

Suspension,  center  of,  138. 
Sympathetic  vibrations,  189. 
Synthesis  of  light,  264. 

Telegraph,      electric,      447;       key, 

447;    signals,  449;    system,  449; 

wireless,  453. 
Telephone,  451. 
Telescope,  astronomical,  257 ; 

Galileo's,  258. 

Temperature,  280;  measuring,  281. 
Tempered  scale,  198. 
Tempering,  15,  199. 
Tenacity,  12. 
Thermal  capacity,  297. 
Thermometer,    282;     clinical,    285; 

limitations  of,  285 ;   scales,  283. 
Thermo-siphon,  system  of  cooling, 

462. 

Throttle  lever,  in  a  motor  car,  471. 
Thunder,  358. 
Time,  22. 

Timer,  in  a  motor  car,  465. 
Tires,  467,  468. 

Tone,  fundamental,  202;  partial,  204. 
Torricellian  experiment,  67. 


Transformers,  435 ;  cut  facing  page 

439. 

Translucent  bodies,  214. 
Transmission,    of     heat,     267 ;      of 

power,  437 ;    in  a  motor  car,  469, 

470. 

Transmitter,  447,  452. 
Transparent  bodies,  214. 
Transverse  vibrations,  176. 
Trombone,  205. 
Tuning  fork,  190. 
Turnbuckle,  174. 

Twelve-cylinder  engine,  460,  462. 
"  Twin-six,"  460. 

Units,  16 ;  of  heat,  297 ;  of  length, 
17;  of  mass,  21 ;  of  time,  22. 

V-type  engine,  463. 
Vacuum,  Torricellian,  67. 
Vaporization,  302 ;   heat  of,  265. 
Velocity,  92;    composition  of,   113; 

of  light,   215 ;    of  molecules,  27 ; 

of  sound,  184;   resolution  of,  113. 
Ventral  segments,  204. 
Vertical  line,  123. 
Vibration,       amplitude       of,      138; 

complete,      138;       forced,      188; 

longitudinal,      177 ;      of     strings, 

201 ;   period  of,  138  ;    single,  138  ; 

sympathetic,       189 ;      transverse, 

176. 

Viscosity,  39. 
Volt,  381. 
Voltaic    cell,    361 ;     electrochemical 

action  in,  363. 
Voltameter,  381. 
Voltmeter,  396. 

Water,  gauge,  49 ;  supply,  50 ; 
waves,  180. 

Watt,  148. 

Wave  motion,  177. 

Waves,  177;  longitudinal,  179; 
electric,  454  ;  length,  180 ;  sound, 
183  ;  transverse,  177  ;  water,  180. 


INDEX  9 

[References  are  to  pages,] 

Wedge,  172.  Whispering  gallery,  188. 

Weight,  9,  122;    of  air,  65;  varia-       Wireless  telegraphy,  453;     teleph- 

tion  of,  124.  ony,  459. 

Welding,  cut  facing  page  16.  Work,   143  ;    units  of,   144  ;    useful, 

Weston  normal  cell,  382.  159  ;  wasteful,  159. 

Wheatstone's  bridge,  391.  X-rays,  414. 
Wheel  and  axle,   164;    mechanical 

advantage  of,  164.  Lrd'  18' 

Wheels,  of  a  motor  car,  467.  Zeppelin,  81,  82. 


YB  360C6 


459995 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


